Ultra sensitive silicon sensor millimeter wave passive imager

ABSTRACT

Electro-thermal feedback is utilized for zeroing the thermal conductance between a bolometer type detector element of a pixel in a thermal radiation sensor assembly and the environments through its mechanical support structure and electrical interconnects, thereby limiting the thermal conductance primarily through photon radiation. Zeroing of the thermal conductance associated with the mechanical support and electrical readout interconnect structures is achieved by electro-thermal feedback that adjust the temperature of an intermediate stage by the heating effect of a bipolar transistor amplifier circuit so that the temperature across the mechanical support and electrical interconnects structures are zeroed thereby greatly improving the thermal isolation, the responsivity and sensitivity of the electromagnetic radiation sensor.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates generally to bolometer type sensors for detectingthermal radiation and more particularly to ultra sensitive siliconbolometer type sensors usable for passive or active imaging atmillimeter (MM) wavelengths.

2. Description of Related Art

Infrared (IR) bolometers are used and proposed for use in many newapplications. The principal application is construction of thermalcameras. Interest in bolometers stems from the fact that theirperformance has significantly improved, they're sensitive at much longerwavelengths, and offer higher operating temperatures. Specifically, IRcameras, with large bolometer arrays have achieved a sensitivity, aNoise Equivalent Temperature resolution (NEΔT) better than ≈0.1K. Suchperformance is less than that of quantum detectors, however, for manyapplications it is adequate and cost effective. Improved bolometerperformance is achieved primarily through improved thermal isolation,made possible with advances in IC micro-machining technology. Thethermal isolation achieved is about an order of magnitude from radiationlimited isolation.

Bolometers inherently operate at slower rates than quantum detectors.However, with staring focal plane arrays, the slow speed limitation isalleviated, since the pixel integration times correspond to the framerate, and is much longer than line times in scanning systems. Thus themain obstacle to making bolometers more sensitive are practicallimitations in thermally isolating each pixel element. With improvedthermal isolation, the bolometers performance will directly improve andthereby find wider applications, including potential replacement forcryogenic FLIR cameras. With ideal thermal isolation, the anticipatedNEΔT improvement is about an order of magnitude in sensitivity.

LWIR and MWIR silicon bolometers having a new operating mode aredisclosed in U.S. Pat. No. 6,489,615 entitled “Ultra Sensitive SiliconSensor”, issued to Nathan Bluzer, the present inventor, on Dec. 3, 2002.This patent is assigned to the present assignee and is incorporatedherein by reference in its entirely.

In U.S. Pat. No. 6,489,615, electro-thermal feedback is utilized forremoving thermal conductance between an absorber element of a bolometerpixel in a thermal radiation sensor assembly and the environmentsthrough its mechanical support structure and electrical interconnects,thereby limiting the thermal conductance primarily through photonradiation. Zeroing the thermal conductance associated with themechanical support structure and electrical interconnects is achieved byelectro-thermal feedback that adjust the temperature of an intermediatestage and the mechanical support structure as well as the electricalinterconnects to equal the bolometer's absorber element temperature.

SUMMARY

Accordingly it is an object of the present invention to provide animprovement in electromagnetic radiation sensors.

It is a further object of the invention to provide an improvement inradiation sensors for detecting thermal radiation in the millimeter (MM)wave spectrum.

It is yet another object of the invention to provide an ultra sensitivesilicon MM wave sensor including electrothermal feedback for providingpassive imaging of an object through various types of environments.

And it is yet a further object of the invention to provide an ultrasensitive silicon sensor adapted for operation for example at, but notlimited to, 30 GHz, 94 GHz, and 220 GHz.

These and other objects are achieved by a method and apparatus includinga two tier ultra sensitive silicon sensor comprising: a heat bath forthe sensor; an antenna element for receiving thermal radiation; anabsorber element coupled to the antenna element for detecting thermalradiation; and an intermediate stage for thermally isolating theabsorber element from the heat bath. The antenna is directly mounted onthe heat bath approximately coplanar with the absorber element and theintermediate stage. Support elements mutually separate the absorberelement, the intermediate stage, and the heat bath. The intermediatestage includes a electro-thermal feedback circuit including a transistorampifier for reducing the thermal conductivity between the absorberelement and the heat bath by causing the temperature of the intermediatestage to converge to the temperature of the absorber element whendetecting thermal radiation, effectively causing the thermal conductanceof the support elements to attain a minimum conductance value andthereby maximize the sensitivity of the absorber element to the thermalradiation limit. Temperature sensing is achieved by using the forwardvoltage of a diode in place of the heretofore used thermal EMF voltage.A plurality of these sensors are intended to fuse in an imaging array.

Further scope of applicability of the present invention will becomeapparent from the detailed description provided hereinafter. It shouldbe understood, however, the detailed description and the specificexamples, while indicating the preferred embodiments of the inventionare made by way of illustration only, since various changes andmodifications coming within the spirit and scope of the invention willbecome apparent to those skilled in the art from the detaileddescription.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will become more fully understood when consideredin conjunction with the accompanying drawings which are provided by wayof illustration only and are thus not meant to be considered in alimiting sense, and wherein:

FIG. 1 is a diagram illustrative of a conventional bolometer type sensorwhich is attached to a thermal isolation bridge sitting on top of asubstrate including a heat bath;

FIG. 2 is a thermal equivalent circuit for the bolometer shown in FIG.1;

FIG. 3 is an electrical noise equivalent circuit of the sensor shown inFIG. 1;

FIG. 4 is an electrical block diagram illustrative of an electro-thermalfeedback circuit for a bolometer type sensor in accordance with thesubject invention;

FIG. 5 is a diagram illustrative of a two-tier bolometer type sensorillustrative of the preferred embodiment of the subject invention;

FIG. 6 is an electrical circuit diagram illustrative of theelectro-thermal feedback circuit implemented in the bolometer sensorshown in FIG. 5;

FIG. 7 is a thermal equivalent circuit of the embodiment of theinvention shown in FIG. 5;

FIG. 8 is a thermal equivalent circuit for the noise sources due tothermal fluctuations in the embodiment shown in FIG. 5;

FIG. 9 is an electrical circuit diagram of the bipolar transistorcircuitry included in the amplifier shown in FIG. 6;

FIG. 10 is a functional equivalent circuit of the electro-thermalfeedback circuit shown in FIG. 9; and,

FIG. 11 is an electrical circuit diagram of an array of pixels shown inFIG. 5.

DETAILED DESCRIPTION OF THE INVENTION

With improved thermal isolation, performance of bolometers will directlyimprove and thereby open a wider range of applications, such as theapplication of bolometers as passive millimeter (MM) wave staringimagers. Accordingly, means are now presented for greatly improving thethermal isolation in bolometers. This requires within each bolometerpixel, the zeroing of the thermal conductance of an MM pixel between thedetector and its mechanical support and readout structures. Achievingimproved thermal isolation to the radiation limit will lead to at leasta ten-fold improvement in performance. Zeroing the thermal conductanceassociated with the mechanical support and readout structures isachieved in the subject invention by introducing an improvedintermediate stage and electrical-thermal feedback over that shown anddescribed in U.S. Pat. No. 6,489,615 which vary the temperature of theintermediate stage to track changes in the detector's temperaturethereby zeroing the net heat flow through the mechanical support andreadout structures. This electrical-thermal feedback between thetemperatures of the intermediate stage and the detector is achieved,moreover, in an ultra sensitive silicon sensor (USSS) which can be usedin passive millimeter wave imagers. The advantages and performanceprovided by this invention will become evident from the analysis tofollow. We begin by first reviewing the performance and limitations ofconventional bolometers and then follow with the performance andadvantages of the ultra sensitive silicon sensor (USSS).

Conventional Bolometers

A conventional bolometer pixel, and its thermal equivalent circuit, areshown in FIGS. 1 and 2. The bolometer pixel 9, as shown in FIG. 1,includes an absorber element or detector 10, represented by a rectanglewith area that is mechanically supported by a low thermal conductancebridge 12, which sits atop of and is anchored to a thermal bath member14 having a temperature T_(HB). Radiation power hν incident on thedetector 10 from a scene Ts is absorbed and changes the detector'stemperature by δT_(D), from T_(D). As shown in FIG. 2, the detector'sheat capacity is C₁ and the thermal conductance of the bridge 12 to theheat bath 14 is G₁. The scene, at temperature T_(S), is radiating energyhν at the detector 10 and this is represented in FIG. 2 as a thermalcurrent Q_(R). The detector 10, in addition to being mechanicallyattached to the heat bath 14 by the bridge's thermal conductance G₁, isradiating power Q_(D1) and receiving Q_(S1), from the shields, notshown.

For the following analysis which involves the thermal equivalent circuitshown in FIG. 2, radiation power is represented as current source Q₁,Q_(S1) and Q_(R1), the thermal conductance between the heat bath 14 atT_(HB) and detector 10 at T_(D) as a thermal resistance with aconductance G₁. The temperatures T_(S), T_(D), T_(HB) are treated asvoltages. With such an equivalent model, the performance of thebolometer pixel 9 (FIG. 1) can be analyzed with the well developedtechniques used for electronic circuits as follows.

Signal Level in Conventional Bolometers

The detector's signal is dependent on the absorbed incident photon fluxpower, and this is given by Q_(R)=σT_(S) ⁴A_(D)/4F², where σ=5.6697×10⁻⁸W−m⁻²−K⁻⁴, T_(s) is the scene temperature, and F is the optic's F#.Additionally, radiation power is incident onto the detector 10 from theshields, and it is given by Q_(S1)=σT_(HB) ⁴A_(D)[1−1/4F²]. Similarly,the detector 10 radiates power to the environment, and this is given byQ_(D1)=σT_(D) ⁴A_(D). Functional differences between the expression forQ_(R), Q_(D1), and Q_(S1) are because the radiated power is throughdifferent solid angles, accounted for by the lens's F#. Additionally,the detector 10 also conducts thermal energy, through conductance G₁, tothe heat bath 14, at temperature T_(HB).

Analytically, the thermal conditions at the bolometer are representedas:

$\quad\begin{matrix}{{Q_{R} - Q_{D1} + Q_{S1}} = {{{\int_{T_{HB}}^{T_{D}}{{G_{1}(T)}\ {\mathbb{d}T}}} + {\int_{T_{D}}^{T_{D} + {\delta\; T_{D}}}{j\;\omega\;{C_{1}(T)}\ {\mathbb{d}T}}}}\mspace{175mu} = {\sum\limits_{n = 0}^{\infty}\;\left\lbrack {{\frac{\partial^{n}{G_{1}\left( T_{HB} \right)}}{\partial T_{HB}^{n}}\frac{\left( {T_{D} - T_{HB}} \right)^{n + 1}}{\left( {n + 1} \right)!}} + {j\;\omega\frac{\partial{C_{1}\left( T_{D} \right)}}{\partial T_{D}^{n}}\frac{\left( {\delta\; T_{D}} \right)^{n + 1}}{\left( {n + 1} \right)!}}} \right\rbrack}}} & (1)\end{matrix}$

The temperature dependence of G₁(T) and C₁(T) have been included inEquation 1. For conventional bolometers shown, for example, in FIG. 1,it is assumed that the derivatives of G₁(T) and C₁(T) are a weakfunction of temperature and for simplicity only first order terms areretained. At equilibrium, or constant radiation power conditions, thedetector's equilibrium temperature T_(D) ⁰ is obtained from Equation 1,for ω=0, and is given by:

$\begin{matrix}{T_{D}^{0} = {T_{HB} + \frac{Q_{R} + Q_{S1} - Q_{D1}}{G_{1} + {0.5\frac{\partial{G_{2}(T)}}{\partial T}\left( {T_{D}^{0} - T_{HB}} \right)}}}} & (2)\end{matrix}$

Thus, at equilibrium, the detector's temperature will be different fromthe heat bath temperature by the net power flow divided by theconductance G₁, measured at T_(D) ⁰. As expected, the more powerreceived by the detector 10, the higher will be its operatingtemperature, since it is directly proportional to the incident power,Q_(R)+Q_(S1)>Q_(D1). Since Q_(S1) is fixed in temperature, thedetector's temperature will change monotonically with changes in scenetemperature T_(S); and changes in the detector's temperature aremaximized with minimum conductance G₁.

Under dynamic conditions, a detector's operation is characterized byrelating dynamic changes in the scene's temperature δT_(S) to dynamicchanges in the bolometer's temperature δT_(D), about the thermalequilibrium temperature T_(D) ⁰. We assumed that the radiation shield isheld at a constant temperature δT_(HB)=0, hence no contribution are madeby ∂Q_(S1)/∂T=0. Taking the differential of remaining terms in Equation1, at temperature T₁ ⁰, we obtain a relationship between δT_(D) andδT_(S) given by:

$\begin{matrix}{{\delta\; T_{D}} = {\frac{G_{R}}{G_{D1} + G_{2}}\frac{{\delta\; T_{S}}\;}{\left\lbrack {1 + {j\;{\omega\left( \frac{C_{1}}{G_{D1} + G_{1}} \right)}}} \right\rbrack}}} & (3)\end{matrix}$

The other variables in Equation 3 are: G_(R)=∂Q_(R)/∂T_(S)=σT_(S)³A_(D)/F² is the conductance of thermal radiation through space from thescene; G_(D1)=∂Q_(D1)/∂T₁=4σT₁ ³A_(D) is the conductance of thermalradiation through space from the detector.

Equation 3 relates the dynamic changes in the scene's temperature δT_(S)to changes in the detector's temperature change δT_(D). The detector'ssignal δT_(D) is monotonically related to δT_(S), and the maximum signalpossible is when δT_(S)=δT_(D). The attenuation from unity gain isrepresented by coefficient G_(R)/[G_(D1)+G₁]. AC response dependent onthe thermal time constant and is given by the radial frequency(ω_(TM)=[G_(D1)+G₁]/C₁. The signal attenuation occurs because a largefraction of power received from the scene (corresponding the detector'sfootprint on the scene) is drained away through conductances G_(D1) andG₁. For maximum signal, conductances G_(D1) and G₂ should approach invalue G_(R.)

Accordingly, much effort has gone into minimizing the thermalconductance G₁. Geometrical approaches coupled with selecting materialswith poor thermal properties are used toward achieving this goal.Constructing detectors with very small mass minimizes C₁ and ACattenuation. However, the size of C₁ inversely impacts the thermal noiselevel at the detector and, therefore, it should not be made arbitrarilysmall. The maximum signal and minimum noise design criteria, given interms of G_(D1), G₁, and C₁, is developed from the noise analysis givenbelow.

Noise Level in Conventional Bolometers

Several noise sources contribute to the total temperature variance atthe detector 10 and all these contribute and limit the detector'ssensitivity. The noise sources include: (1) variance in the scene'sphoton power absorbed by the absorber element, δQ² _(R), (2) variance inthe photon power emitted by the absorber element, δQ_(D1) ², (3)variance in the radiation shield's photon power absorbed by thedetector, δQ_(S1) ², (4) variance in the thermal bath 14 temperature,δT_(HB) ², and (5) variance in the detector's temperature produced bynoise in readout electronics, δT_(EL) ².

Each of these noise sources causes sensitivity degradation and they areexamined below. The effects of the various noise sources are quantifiedin terms of their contribution to the detector's temperature variance.Quantification in terms of the detector's temperature variances, isappropriate for the bolometer's sensitivity is typically given in termsof noise equivalent temperature resolution (NEΔT). Thus, the photon fluxvariance, from the scene, δQ_(R) ², the detector, δQ_(D1) ², and theshields, δQ_(S1) ², produce temperature variances at the absorberlabeled as: δT_(S) ², δT₁ ², and δT_(S1) ², respectively, and arecomputed below.

(I.) Scene fluctuations in the power emitted increase the detector'stemperature variance. Fluctuations in the scene's output power imposethe ultimate limit on the bolometer's sensitivity, represented in termsof NEΔT. The best, smallest NEΔT is achieved when all other noisesources, including noise from the detector 10, are much smaller thannoise from fluctuations in scene's photon flux. Thus the minimum noiselevel corresponds to the noise variance δQ²R of the signal power Q_(R),arriving from the scene and absorbed by the detector 10, and is givenby:

$\begin{matrix}{{\delta\; Q_{R}^{2}} = \frac{8A_{D}\sigma\; k_{B}T_{S}^{5}\Delta\; f}{4F^{2}}} & (4)\end{matrix}$

where, Δf represents the electrical frequency bandwidth of the detector10 and k_(B) is Boltzmann's constant. The denominator accounts for thefact that only a fraction of the signal reaches the detector 10 and thesize of the fluctuation is reduced as is the photon signal emitted bythe scene.

Fluctuations in the scene output power is readily translated into atemperature variance at the detector 10, and this represents backgroundlimited performance. Temperature variance at the detector induced by thescene δT_(S) ² is obtained by combining Equations 3 and 4 andintegrating over frequency. Specifically, the temperature fluctuationsδT_(S) ², at the detector, is produced by the scene radiation varianceδQ_(R) ² and is given by:

$\begin{matrix}{{\delta\; T_{S}^{2}} = {{\frac{2}{\pi\; F^{2}}{\int_{0}^{\infty}{\frac{A_{D}\sigma\; k_{B}T_{S}^{5}}{\left\lbrack {G_{D1} + G_{1}} \right\rbrack^{2} + {\omega^{2}\left\lbrack C_{1} \right\rbrack}^{2}}\ {\mathbb{d}\omega}}}} = {\frac{G_{R}}{\left( {G_{D1} + G_{1}} \right)} \cdot \frac{k_{B}T_{S}^{2}}{C_{1}}}}} & (5)\end{matrix}$

Equation 5 reveals that the temperature variance, induced by the sceneon the detector 10, is a product of two factors. The first factor is theratio of free space conductance to the conductance between the detector10 and thermal bath 14: G_(R)/[G_(D1)+G₁. The second factor correspondsto the temperature variance of an object at temperature T_(s) and withheat capacity C₁. For best performance, the noise from the scene shoulddominate over all other noise sources. This is facilitated with a fastlens (small F#) and minimum conductance [G_(D1)+G₁] (absorber element 10with good thermal isolation).

(II.) Variance in the detector's temperature δT₁ ² is produced byseveral sources, and this includes: (1) thermal conductance G₁ betweenthe detector 10 and heat bath 14, (2) radiative conductance G_(D1)between the detector 10 and radiation shields, not shown, and (3)radiative conductance G_(S) between the detector 10 and scene, justconsidered. Here, we focus on temperature variances due to thermalconductances G₁, and G_(D1).

At the detector 10, the spectral density of temperature variance δT₁²(f) is given in terms of the different conductance paths between thedetector 10 and surroundings. The expression for the spectraltemperature variance is given as:

$\begin{matrix}{{\delta\;{T_{D}^{2}(f)}} = \frac{4k_{B}{T_{D}^{2}\left\lbrack {G_{1} + G_{D1}} \right\rbrack}}{\left\lbrack {G_{1} + G_{D1}} \right\rbrack^{2} + \left\lbrack {\omega\; C_{1}} \right\rbrack^{2}}} & (6)\end{matrix}$

The integral of Equation 6 yields the thermodynamic expressionk_(B)T_(D) ²/C₁, corresponding to the temperature variance of an objectat T_(D) with a heat capacity C₁. However, this total temperaturevariance includes contributions from radiative and thermal conductancepaths. The radiative part is included by the G_(D1) term in thedenominator of Equation 6. Two contributors are included in G_(D1), onefrom the scene and the other from the radiation shields. Hence,G_(D1)=G_(R)+G_(S1), where G_(S1) is the conductance between theradiation shield and the detector 10. Performing the integration withrespect to radial frequencies ω, we obtain for δT_(D) ²:

$\begin{matrix}{{\delta\; T_{D}^{2}} = {{\frac{1}{2\pi}{\int_{0}^{\infty}{\frac{4k_{B}{T_{1}^{2}\left\lbrack {G_{1} + G_{D1}} \right\rbrack}}{\left\lbrack {G_{1} + G_{D1}} \right\rbrack^{2} + \left\lbrack {\omega\; C_{1}} \right\rbrack^{2}}\ {\mathbb{d}\omega}}}} = \frac{k_{B}T_{D}^{2}}{C_{1}}}} & (7)\end{matrix}$

Thus the detector's temperature variance, δT₁ ², reduces to thetheoretical temperature variance of an object at temperature T_(D) andwith a heat capacity of C₁.

(III.) Fluctuations in power from the antenna 20 and housing (radiationshield), surrounding the absorber element, contribute to the overalltemperature variance. Photons from the antenna 20 are indistinguishablefrom photons form the scene, represented by Equation 4. The temperaturevariance, produced by these fluctuations, is readily estimated in termsof the radiation conductance between the detector 10 and shield,G_(S1)=G_(D1)−G_(R). Proceeding as with Equations 6 and 7, theexpression for temperature variance δT_(S1) ², at the detector 10, dueto the radiation shield held at temperature T_(S1), becomes:

$\begin{matrix}{{\delta\; T_{S1}^{2}} = {{\frac{1}{2\pi}{\int_{0}^{\infty}{\frac{4k_{B}{T_{S1}^{2}\left\lbrack {G_{D1} - G_{R}} \right\rbrack}}{\left\lbrack {G_{1} + G_{D1}} \right\rbrack^{2} + \left\lbrack {\omega\; C_{1}} \right\rbrack^{2}}\ {\mathbb{d}\omega}}}} = {\left\lbrack \frac{G_{D1} - G_{R}}{G_{1} + G_{D1}} \right\rbrack\frac{k_{B}T_{S1}^{2}}{C_{1}}}}} & (8)\end{matrix}$

The temperature variance δT_(S1) ² is given as a product of two factors.The first factor indicates that this contribution is attenuated by theratio of G_(S1)=G_(D1)−G_(R) to the total conductance, G_(S1)+G_(D2).The second factor is the theoretical temperature variance of an objectat temperature T_(S1) and with a heat capacity of C₁. Typically, theradiation shield's temperature equals to the heat bath 14 temperature,T_(HB). Hence, we typically substitute T_(HB) for T_(S1), in Equation 8.

(IV.) Thermal bath fluctuations contribute to the variance in detector's10 temperature. The temperature variance δT_(HB) ² in the temperature ofthe heat bath 14 T_(HB) (FIG. 1) is given as:

$\begin{matrix}{{\delta\; T_{HB}^{2}} = \frac{k_{B}T_{HB}^{2}}{C_{HB}}} & (9)\end{matrix}$

-   -   where, C_(HB) is the heat capacity of the heat bath 14. The        variance δT_(HB) ² can be made small by increasing the mass of        the heat bath 14, and in principle this can make δT_(HB) ²        arbitrarily small relative to the other noise sources. This is        particularly important, for the temperature variance in the heat        bath is directly coupled to the detector 10. Typically,        G₁>>G_(R), G_(D1), and G_(S1). Hence, with the equivalent        circuit in FIG. 2 this provides direct evidence that the        variance δT_(HB) ² modulates the detector's temperature with a        coupling coefficient approaching unity. Thus, for all practical        purposes, the temperature variance in the heat bath 14        replicates itself as a variance in the absorber element's        temperature and is given by Equation 9.

(V.) Noise in the detector's readout circuits contribute to thedetector's temperature variance. The readout circuit noise is given by avoltage squared spectral density dE_(NA) ²/df, which includes 1/f andwhite noise components. In this analysis, this voltage noise istranslated to an equivalent variance in temperature at the bolometer.This translation from variances in voltage to variances in temperaturefacilitates the analysis and the computation of NEΔT. Translating thereadout circuit's voltage noise into an equivalent variance intemperature requires consideration of the actual readout circuits andthe bolometer. In this analysis, consistent with the fact that resistivebolometers are the most widely used, we analyze the performance of aconventional resistive bolometer.

Resistive Bolometer

The readout circuit's voltage noise corrupts the output from a resistivebolometer, biased with a dc current I_(CR). For improved understanding,the corruption produced by electronic circuit noise is transformed intoan equivalent temperature variance. This equivalent variance in theabsorber element's temperature, caused by electronic voltage noise, islabeled as δT_(EL) ².

The total electrical noise presented at the readout circuit, shown inFIG. 3, is a sum of spectral voltage noise variances from the bolometerdE² _(N)/df and amplifier dE² _(NA)/df. The voltage noise from thebolometer is filtered by the circuit capacitance C_(E), and is in serieswith the noise form the amplifier. The equivalent temperature varianceproduced by the voltage noise at the readout amplifier's input is:

$\begin{matrix}{{\delta\; T_{EL}^{2}} = {{\frac{1}{\left\lbrack {I_{CR}\frac{\partial R_{CB}}{\partial T_{S}}} \right\rbrack^{2}} \cdot \frac{1}{2\pi}}{\int_{0}^{\infty}{\left\lbrack \ {\frac{\frac{\mathbb{d}E_{N}^{2}}{\mathbb{d}f}}{1 + \left( {\omega\; C_{E}R_{E}} \right)^{2}} + \frac{\mathbb{d}E_{NA}^{2}}{\mathbb{d}f}} \right\rbrack{\mathbb{d}\omega}}}}} & (10)\end{matrix}$

where, the leading factor in Equation 10 converts the variance involtage noise to a temperature variance by dividing byI_(CR)∂R_(CB)/∂T_(S), squared, where ∂R_(CB)/∂T_(S) represents theresistive temperature coefficient, and I_(CR) is the dc bias currentflowing through the bolometer during readout. The second factor inEquation 10 contains the variances of the bolometer and the amplifier'svoltage noise spectral density.

For best performance, the bolometer's resistive temperature coefficient∂R_(CB)/∂T_(S) should be made large, for this directly attenuates thecontributions of voltage noise to the temperature variance. See Equation10. Making the bolometer's dc bias current I_(CR) large, helps inprinciple, but has practical problems in that the associated I²R heatingis much larger (>1000×) that the IR signal and requires pulsed operation(wider noise bandwidth) of the absorber element's readout circuits.Additional noise reduction is achieved by selecting readout amplifierswith spectral voltage variances dE² _(NA)/df smaller than thebolometer's dE² _(N)/df. Such conditions are facilitated with largeresistance bolometers. Typically, the bolometer's resistance is greaterthan 10KΩ, which represents a white noise voltage spectral density of12.9 nV/Hz^(1/2). This value does not include 1/f noise terms whichcomplicate the integration of Equation 10. If we assume that only thewhite noise from the bolometer dominates, then Equation 10 can bereadily integrated and the result is given by:

$\begin{matrix}{{\delta\; T_{EL}^{2}} = {\frac{1}{\left\lbrack {I_{CR}\frac{\partial R_{CB}}{\partial T_{S}}} \right\rbrack^{2}} \cdot {\frac{0.25}{C_{E}R_{E}}\left\lbrack \frac{\mathbb{d}E_{N}^{2}}{\mathbb{d}f} \right\rbrack}}} & (11)\end{matrix}$

For the purpose of calculations, we can increase the value of d E_(N)²/df to compensate for 1/f noise components, and we choose to use 0.1μV/Hz^(1/2) for the value of d²E_(N)/df. It should be also noted thatthe value of Equation 11 is proportional to the electrical readoutbandwidth given as (ω_(EL)=1/C_(E)R_(E). Ideally, ω_(EL) should equalthe thermal mechanical bandwidth ω_(TM)=[G_(D1)+G₁]/C₁. Typically, thethermal mechanical bandwidth is narrower than the electrical readoutbandwidth (ω_(EL)>ω_(TM)) by a constant factor K_(BW), so that(ω_(EL)=K_(BW)ω_(TM).

The bolometer's total temperature variance δT_(T) ² is simply the sum ofEquations 5, 7, 8, 9 and 10. If we assume d E_(N) ²/df is constant withfrequency and after some rearrangements, the equation for δT_(T) ² isgiven by:

$\begin{matrix}{{\delta\; T_{T}^{2}} = {\left( \frac{k_{B}T_{S}^{2}}{C_{1}} \right) \cdot \left( \frac{G_{R}}{G_{D1} + G_{1}} \right) \cdot \left\{ {1 + {\left( \frac{G_{1} + G_{D1} - G_{R}}{G_{R}} \right)\frac{T_{D}^{2}}{T_{S}^{2}}} + {\frac{C_{1}}{C_{HB}}\left( \frac{G_{R} + G_{1}}{G_{R}} \right)\frac{T_{HB}^{2}}{T_{S}^{2}}} + {\left( \frac{G_{R} + G_{1}}{G_{R}} \right)\frac{C_{1}}{k_{B}T_{S}^{2}}\frac{\frac{0.25}{C_{E}R_{E}}\frac{\mathbb{d}E_{N}^{2}}{\mathbb{d}f}}{\left( {I_{CR}\frac{\partial R_{CB}}{\partial T_{S}}} \right)^{2}}}} \right\}}} & (12)\end{matrix}$

Equation 12 had been cast into this form to reveal the relative valuesof every noise source relative to the noise present in the signal.Equation 12 is made up of a product of three terms. The leading factoris the minimum thermodynamically possible temperature variance at adetector, limited by the detector's heat capacity and scene temperature.The second factor shows how this minimum temperature variance isincreased since the detector's thermal isolation is not as good as theconductance between the scene and the detector. The third factor, in thebraces, includes different noise sources which increase the absorberelement's overall temperature variance. When the expression in thebraces equals one, the dominant noise is scene noise.

The temperature resolution of the bolometer is limited by the variance,given by Equation 12, and is simply equal to the standard deviation: thesquare root of Equation 12. Combining this with the signal amplitude(given by Equation 3) the bolometer's performance is determined. Thebolometer's performance in terms of NEΔT is calculated below.

Sensitivity of Conventional Bolometers

The sensitivity of bolometers is given in terms of their temperatureresolution NEΔT. The NEΔT is the minimum temperature the bolometer canresolve and occurs when the absolute signal to noise ratio is unity. Thesignal to noise ratio is readily calculated with Equations 3 and 12. Thesignal to noise ratio equals the signal induced temperature change inthe bolometer, given by Equation 3, divided by the RMS fluctuation inthe bolometer's temperature, given by the square root of Equation 12.For unity signal to noise ratio, solving for δT_(S), the equationobtained for NEΔT is:

$\begin{matrix}{{{NE}\;\Delta\; T} = {\sqrt{\frac{\omega_{TM}k_{B}T_{S}^{2}}{G_{R}}}\sqrt{1 + \left( \frac{\omega}{\omega_{TM}} \right)^{2}}\left\{ {1 + {\left( \frac{G_{1} + G_{D1} - G_{R}}{G_{R}} \right)\frac{T_{D}^{2}}{T_{S}^{2}}} + {\frac{C_{1}}{C_{HB}}\left( \frac{G_{D1} + G_{1}}{G_{R}} \right)\frac{T_{HB}^{2}}{T_{S}^{2}}} + {\frac{C_{2}}{k_{B}T_{S}^{2}}\left( \frac{G_{D1} + G_{1}}{G_{R}} \right)\frac{\frac{\omega_{EL}}{4}\frac{\mathbb{d}E_{N}^{2}}{\mathbb{d}f}}{\left( {I_{CR}\frac{\partial R_{CB}}{\partial T_{S}}} \right)^{2}}}} \right\}^{1/2}}} & (13)\end{matrix}$

The expression for NEΔT has been simplified by incorporating intoEquation 13 ω_(TM)=[G_(D1)+G₁]/C₁ and ω_(EL)=1/R_(E)C_(E). Thus, NEΔT isexpressed as a product of three factors. The first factor represents thelow frequency thermodynamic sensitivity limit determined by: the thermalbandwidth ω_(TM), and G_(R), dependent on the optics F#, the detectorsize A_(D), and the scene temperature T_(S). The second factor indicateshow the sensitivity decreases with frequency (ω_(TM)=[G₁+G₁]/C₁. Thethird factor includes the contributions from various noise sources: (1)noise in the scene signal, (2) noise from the bolometer, includingradiation shields, (3) noise from the thermal bath, and (4) noise fromthe electronic readout circuits.

The NEΔT is expressed as a product of three factors in Equation 13.Maximum sensitivity, i.e., the smallest NEΔT, is achieved by minimizingeach of these factors. The middle factor in Equation 13 represents theradial frequency dependence of NEΔT. Optimally, the thermal radialcut-off frequency ω_(TM) should be made equal to the system frame rate.Setting ω_(TM) at the system frame rate will maximize the system's dcsensitivity and this is evident from the first factor in Equation 13.The First factor in Equation 13 dictates that for maximum sensitivity:(1) ω_(TM) be set at a minimum, (2) the optics F# should be as small aspossible (fast optics), and (3) the absorber's size A_(D) should be aslarge as possible, while satisfying system resolution requirements. Thethird factor explicitly includes all the noise terms and for bestsensitivity it should be minimized to unity.

The steps required to minimize the third factor to unity are revealed byexamining in detail each of the noise terms. The noise: terms in thethird factor are divided into three groups. The first group representsradiation noise from the scene and the absorber (including radiationshields) noise. The minimum noise occurs if the scene noise dominates.This is facilitated by using a small F# (fast optics), operating thedetector T_(D) and radiation shields T_(HB) colder than the scenetemperature T_(S); however, for equilibrium detectors this is notpossible since ideally the detector and scene are in thermalequilibrium.

The middle term in the third factor in Equation 13, represents heat bathnoise contributions, coupled through thermal contact G₁, to thedetector. Reduction of the heat bath noise contributions are readilyminimized by making C_(HB)>>C₁. By making the heat capacity sufficientlylarge, the heat bath noise is severely reduced and no other steps areneeded to achieve further reductions.

The bottom term in the third factor in Equation 13 represents thereadout electronics noise contribution to the detector. Reducing thereadout electronics noise below the scene noise in the signal isdifficult. The difficulty becomes evident by quantitively examining thebottom term in third factor in Equation 13. Optimistically, let's assumethat the noise from the resistive bolometer dominates, and typically fora 10⁴Ω resistor the noise dE_(N) ²/df is about 2×10⁻¹⁶V²/Hz. This doesnot include 1/f noise that makes things even worse. In resistivebolometers, ∂R_(CB)/∂T_(S)≈200Ω/K and G₁/G_(D1)10. For: T_(S)≈300K,T₁≈213K, A_(D)=0.25×10⁻⁴ cm², and F=1; we evaluate the bottom term inthe third factor in Equation 13, and obtain:(ω_(EL)/ω_(TM))1.3×10⁻⁹/I_(CR) ². This expression, for the electronicnoise contribution, should be significantly less than 1 to makeelectronic noise insignificant. If (ω_(EL)/ω_(TM))=1, the requiredcircuit current I_(CR)>>0.04 mA. If the 1/f noise is included, therequired current level is probably I_(CR)>1 mA. With I_(CR)≈1 mA, duringreadout, the I²R power delivered is about 10 mWatts, verses 0.1 μWattsdelivered from the scene This means the readout I²R power is 100thousand times greater then the power in the signal. This isunacceptable for it introduces thermal stability problems, which can bereduced by reducing readout circuits operational duty cycle. In astaring array, with 400×500 elements, for example, the readout dutycycle can be reduced by up to 2×10⁵ fold to alleviating thermalproblems. However the noise bandwidth is increases inversely withreadout duty cycle whereas readout noise decreases as a square of thereadout current I_(cr), i.e., (ω_(EL)/ω_(TM))1.3×10⁻⁹/I_(cR) ². Thissolution has practical limitations due to the current capacity of thebolometer and the readout circuit's maximum voltage compliance. Thus,increasing the I_(CR) and decreasing the duty cycle providesinsufficient improvements but has practical limitations.

It should be emphasized that the analysis presented for IR bolometers ismuch less demanding compared to passive MM wave imaging. This can beappreciated by examining Equation 12 where all the noise terms arerepresented at the detector as temperature variances. In the IR case,G_(R)≅, 10⁻⁹ W/K and G₁≅2×10⁻⁸ W/K. Hence the temperature variance willincrease by at least [G₁/G_(R)]²≅100, and this is not includingelectronic noise. In the MM wave region the equivalent value of G_(R) isreplaced by G_(AE)≅4×10⁻¹² W/K. The corresponding minimum increase inthe temperature variance will increase as [G₁/G_(AE)]²≅6×10⁶ or morethan 1000 times. This translates the sensitivity of conventional LWIRbolometers from about 25 mK to 25 Kelvin. If electronic readout noise isincluded, the situation will get even worse. These sensitivitylimitations can be overcome with the USSS approach and it is describedin the next section.

MM Ultra Sensitive Silicon Sensor

It is evident from the previous discussion on NEΔT (see Equation 13)that the bolometer's sensitivity is reduced by the ratio(G_(D1)+G₁]/G_(R). Similarly, the photoresponse amplitude, see Equation3, is also degraded by the ratio G_(R)/(G_(D1)+G₁]. Since G_(D1) andG_(R) are limited by the optics, performance improvements requires thereduction of the thermal conductivity G₁ between the absorber element 10and the heat bath 14 in FIG. 1. Much effort has been invested intominimizing thermal conductivity G₁ by utilizing special materials andgeometries. Presently, the value achieved for G₁2×10⁻⁸ Watts/K, and thisis about ten times larger than G_(D1). In fact, what is needed, is forG₁ to be ten times smaller than G_(D1). Given the limitations inherentwith material and geometrical approaches, further reductions in G₁,thermal conductivity between the bolometer and heat bath, require adifferent approach.

The present invention is directed to an improved approach whereby anultra sensitive silicon sensor (USSS), included, for example, in anarray of pixels (FIG. 11) is fabricated using only silicon technologyand electro-thermal feedback is used to substantially reduce the thermalconductivity G₁. With the electro-thermal feedback, a ten foldimprovement in the thermal isolation of the bolometer pixel can beachieved, with: (1) associated improvements in NEΔT; and (2) an increasein photoresponse amplitude. The operation and performance advantages ofan MM-USSS are detailed below.

We begin by elaborating how electro-thermal feedback provides at least aten fold reduction in thermal conductivity over prior art approachesbased only on optimally low conductivity materials and geometries. Thisexplanation is followed by a calculation of the photoresponse and noiselevels of a passive MM-USSS. From these calculations, the MM-USSSsensitivity is computed.

Maximum Thermal Isolation Through Electro-Thermal Feedback

Thermal isolation between the absorber element 10 of a bolometer pixel 9and heat bath 14 shown in FIG. 1 can be significantly improved with theuse of electro-thermal feedback. The concept of electro-thermal feedbackhas been disclosed in the above referenced Bluzer patent, U.S. Pat. No.6,489,615. Maximizing thermal isolation through electro-thermal feedbackin accordance with the subject invention will now be demonstrated byanalysis. The analysis of the MM-USSS in accordance with the subjectinvention will include ac and dc components; however, for simplicity andclarity, the analysis is limited to a dc response.

Referring now to FIGS. 4–6, shown thereat is a bolometer pixel 9including an absorber element or detector 10, at temperature T_(D),thermally connected to the heat bath 14, at temperature T_(HB), thoroughan intermediate stage 16 at temperature T_(IN). We assert that by designT_(HB) is always less than T_(D) and T_(IN). In addition to normaleffects, the relationship between T_(D) and T_(IN) is most influenced byan electro-thermal feedback circuit, represented by an amplifier 18. Theamplifier 18 is used to generate heat Q_(H) in the intermediate stage16. The generated heat is proportional to the difference betweentemperatures T_(D) and T_(IN), specifically, Q_(H)=A(T_(D)−T_(IN)),where A is the electrical-thermal feedback constant.

The detector 10 at temperature T_(D) receives radiation in severaldifferent ways. In the present invention, the detector 10 receivesmillimeter (MM) wave radiation Q_(AE) from the scene indirectly from anac coupled antenna 20 as shown in FIG. 5 and directly by absorbing blackbody radiation Q_(D). Also, the detector 10 at temperature T_(D)receives radiation Q_(S1) from the shields and radiates itself into theenvironment Q_(D1). The intermediate stage also radiates thermalradiation Q_(D2) while receiving thermal radiation Q_(S2) from theradiation shields. Additionally, links G₁=G_(1A)+G_(1B) andG₂=G_(2A)+G_(2B), shown as resistive elements 22, 24 and 26, 28,thermally and electrically interconnect the bolometer pixel 9; thedetector 10, the intermediate stage 16, and the heat bath 14, as shown.The effective thermal impedance between the detector 10 and thesurrounding includes the effect of electro-thermal feedback. The effectof electro-thermal feedback on thermal isolation is calculated from heatconservation equations. The dc heat conservation equation at theintermediate stage 16 is:(T _(D) −T _(IN))G ₁ +Q _(H) +Q _(S2) =Q _(D2)+(T _(IN) −T _(HB))G₂  (14)

Since the radiation shields and the heat bath 14 are held at the sameconstant temperature, the terms Q_(S2) and T_(HB) are constant inEquation 14. Taking the differential of Equation 14, the relationshipbetween temperatures T_(D) and T_(IN) is computed and is given by:

$\begin{matrix}{{\delta\; T_{IN}} = {\frac{\left( {G_{1} + A} \right)}{\left( {G_{1} + G_{2} + G_{D2} + A} \right)}\delta\; T_{D}}} & (15)\end{matrix}$

where G_(D2)=∂Q_(D2)/∂T_(IN) is the radiative conductance from theintermediate stage to it's surroundings, and is given byδQ _(D2) =G _(D2) δT _(IN)=8σA _(IN) T _(IN) ³ δT _(IN)  (16)

With A_(IN) is the intermediate stage front surface area, andσ=5.6697×10⁻⁸ W/M²−K⁴, the Stefan-Boltzmann constant. It should be notedfrom Equation 15 that if the electrical-thermal feedback constant A issufficiently large, relative to G₁, G₂, and G_(D2), any temperaturechanges in δT_(D) are tracked and almost replicated by δT_(IN). Theeffect of changes in the apparent scene temperature δT_(S), on thedetector's δT_(D), is obtained from heat conservation at the detectorand is given by:Q _(AE) +Q _(D) +Q _(S1) =Q _(D1)+(T _(D) −T _(IN))G ₁  (17)

Before taking the differential of Equation 17, we proceed to examineeach term. The right side of Equation 17 includes the black bodyradiation Q₁ given off by the detector 10, and the power drained throughconductance G₁. The differential power radiated directly by the detector10 is given by:δQ _(D1) =G _(D1) δT _(D)=8σA _(D) T _(D) ³ δT _(D)  (18)

Where A_(D) represents the detectors front surface area. The left handside of Equation 17 includes three terms, one constant and two variableterms. The term Q_(S1) (δQ_(S1)=0) is a constant since the shields aremaintained at a constant temperature. The variable terms Q_(D)represents the black body radiation received by the detector 10 directlyand its differential is given as:

$\begin{matrix}{{{\delta\; Q_{D}} = {{G_{D}\delta\; T_{S}} = {\frac{2\sigma\; A_{D}T_{S}^{3}}{F^{2}}\delta\; T_{S}}}}\;} & (19)\end{matrix}$

where, F is the optics F-number and Ts is the actual change in scenetemperature. The term Q_(AE) represents the MM wave radiation receivedby the detector 10 from the antenna 20. Since the MM wave energyhν<<kT_(S), the Planck expressions can be simplified. Integrating theradiation received over the operating frequency bandwidth, we obtain asimple expression and it is given by:

$\begin{matrix}{Q_{AE} = \frac{{ɛ\eta}\; A_{P}{{kT}_{S}\left( {v_{2}^{3} - v_{1}^{3}} \right)}}{3{F^{2}\left( {c/N} \right)}^{2}}} & (20)\end{matrix}$

Where: “k” is Boltzmann's constant; “η” represents the antennaefficiency; “c” is the speed of light. “N” is the index of refraction;“ν₂−ν₁” is the operating bandwidth of the antenna 20; A_(P) is theantenna area and is substantially equal to the pixel area; ε is theobjects emissivity; and T_(S) is the scene temperature.

In IR the emissivity is approximated as unity. In the MM wave region theemissivity changes and we can assume, conservatively, that theemissivity varies about δε/ε≅10%. Taking the differential of Q_(AE) andincluding contributions from emissivity and scene temperature variationswe obtain:

$\begin{matrix}{{\delta\; Q_{AE}} = {{\frac{\eta\; A_{P}{k\left( {v_{2}^{3} - v_{1}^{3}} \right)}}{3{F^{2}\left( {c/N} \right)}^{2}}\left( {{{ɛ\delta}\; T_{S}} + {T_{S}{\delta ɛ}}} \right)} \cong {\frac{\eta\; A_{P}{k\left( {v_{2}^{3} - v_{1}^{3}} \right)}}{3{F^{2}\left( {c/N} \right)}^{2}}\left( {{\delta\; T_{S}} + {T_{S}{\delta ɛ}}} \right)}}} & (21)\end{matrix}$

The right side of equation 21 include a term δT_(S)+T_(S)δε=δT_(SS)where we define δT_(SS) as the equivalent radiometric temperature. Itshould be noted that the equivalent radiometric temperature can be muchlarger that the actual change in temperature δT_(S). In this analysisfor mm wave performance we will be always using the equivalentradiometric temperature T_(SS). Taking the differential of Equation 17,we obtain a relationship between changes in the apparent scenetemperatures T_(SS), the detector's temperature T_(D), and intermediatestage temperature T_(IN) and these are given by:G _(AE) δT _(SS) +G _(D) δT _(S)=(G _(D1) +G ₁)δT _(D) −G ₁ δT_(IN)  (22)

Where G₁=∂Q_(D1)/∂T_(D) G_(D)=∂Q_(D)/∂T_(S). As will become evidentlater, we neglect G_(D) because G_(D)<G_(AE). Combining Equations 15 and17, the intermediate stage temperature differential, δT_(IN), iseliminated, and we obtain a relationship between δT_(SS) and δT_(D)given by:

$\begin{matrix}{{\delta\; T_{D}} = {{\frac{G_{AE}}{G_{D1} + {G_{1}\left( \frac{G_{2} + G_{D2}}{G_{1} + G_{2} + G_{D2} + A} \right)}}\delta\; T_{SS}} \approx {\frac{G_{AE}}{G_{D1} + \frac{G_{2}G_{1}}{A}}\delta\; T_{SS}}}} & (23)\end{matrix}$

The advantages of electrical-thermal feedback are illustrated byEquation (23). For a large electrical-thermal feedback constantA[A>>{G₁, G₂, G_(D2)}], the denominator in Equation 23 reduces toG_(D1). If no electrical-thermal feedback were utilized [A=0] thedenominator in Equation 23 increases to G_(D1)+G₁G₂/(G₁+G₂)−0.5G₁. Thuslarge electrical-thermal feedback severely attenuates the thermalshunting effects produced by G₁ and G₂, thereby effectively increasingthe detector's thermal isolation from 0.5G₁ to G_(D1). The increase inthermal isolation is best appreciated if we numerically examine Equation(23).

The numerical values of G_(AE), G₁, G₂, G_(D1), G_(D) and G_(D2), arecomputed with Equations 16, 18, 19, 21. The values for G₁ and G₂, basedon experience, are approximated as 10G₁≈G₂≈10⁻⁷ W/K. We compute (detailsfollow) for A≈10⁻⁵ W/K. For A_(P) representing a 1 MM square pixelcoupled through an antenna 20 (see FIG. 5) and a lens, not shown, withan index of refraction N=10 and F=1, we obtain G_(AE)≅4.2×10⁻¹²W/K[assuming a 30 GHz bandwidth, centered at 95 GHz and 100% couplingefficiency]. The detector at temperature T_(D) will be made small about5 μm in diameter. It follows that G_(D)≅6×10⁻¹¹ W/K and G_(D1)≅2.4×10⁻¹⁰W/K. The value of G_(D2)≅2.4×10⁻⁹ W/K because the intermediate stagewill be about 10 times larger in size than the detector. Gathering thesenumerical values, we examine the two limits of Equation 23: with andwithout electrical-thermal feedback and obtain:

$\begin{matrix}{{\delta\; T_{D}} \approx \begin{Bmatrix}{12 \times 10^{- 3}T_{SS}} & {{with}\mspace{14mu}{feedback}} \\{42 \times 10^{- 6}T_{SS}} & {{no}\mspace{14mu}{feedback}}\end{Bmatrix}} & (24)\end{matrix}$

Equation (24) dramatically illustrates the effect of electrical-thermalfeedback: for a given change in equivalent radiometric temperature,δT_(SS), the response signal at the detector, δT_(D), is increased morethan 250 fold because of greatly diminished effects of thermal loadingon the detector.

Using the principal of electro-thermal feedback, improved thermalisolation is achieved and the degree of isolation achieved is beyond theisolation possible through optimizing thermal insulating by materialsand/or geometrical approaches. Incorporating the principal ofelectro-thermal feedback, we proceed to present and analyze theperformance of a millimeter (MM) wave ultra sensitive silicon sensor(USSS) pixel in accordance with the subject invention.

MM USSS Pixel Embodiments and Operating/Readout Electronics

Incorporation of electro-thermal feedback to form an ultra sensitivesilicon sensor in accordance with the subject invention as shown inFIGS. 5, 6 and 9 requires combining special circuits within eachbolometer pixel 9. Specifically, electro-thermal feedback requires: (1)a temperature difference sensor, (2) a temperature difference amplifier,(3) a heater with an output dependent on temperature difference, and (4)a structure which incorporates items 1 through 3 into a single pixel.

With respect to (4) above, in FIG. 5, the USSS pixel 9 in accordancewith the subject invention utilizes a two-tier design for simplifyingfabrication and maximizing area efficiency, and is shown including adetector element 10 at T_(D) ac coupled via ac coupling means 11 to anantenna 20, and having a flat upper absorber portion with apredetermined surface area, an intermediate stage 16 at T_(IN) adjacentto the detector element 10 and a heat bath 14. The heat bath at T_(HB)includes a substrate portion 15 and an annular upper body portion.Support elements or links 22, 24 and 26, 28 respectively couple thedetector 10 to the intermediate stage 16 and the intermediate stage 16to the upper portion 17 of the heat bath 14, providing conductancesG_(1A) and G_(1B) and G_(2A) and G_(2B). The intermediate stage 16 andthe detector 10 are substantially coplanar and are mounted in agenerally circular cavity 30 of the upper body member 17 of the heatbath 14 being secured to the inner wall surface 32 via the supportelements 26 and 28. The antenna element 20 is shown comprising agenerally flat member located on the outer surface 34 of the upper bodymember 17 of the heat bath 14 and is substantially coplanar with thedetector element 10 and the intermediate stage 16.

The USSS pixels 9 shown in FIGS. 5 and 9 are intended for incorporationinto an array with readout electronics for accessing the output of eachindividual pixel. An x-y array of pixels 9 is shown in FIG. 11 andincludes x-y address switches 42 and 44 for reading out each pixel 9.Conventional address circuits, column and row shift registers utilizedwith such an array are not shown. Such an array is capable of passivelyimaging electromagnetic radiation emanating from a scene, for example,at millimeter wavelengths.

Since operation is intended for imaging in the millimeter (MM) waveportion of the electromagnetic spectrum, the pixel size of a pixel 9, asshown in FIG. 5, is on the order of 250 times the size of a pixel shownand described in the above referenced U.S. Pat. No. 6,489,615 and whichis intended primarily for operation at LWIR.

The temperature difference sensor in the subject invention utilizes twosilicon diodes 30 and 40 connected back to back, to measure thetemperature difference between the detector 10 and the intermediatestage 16. One diode 38 is incorporated in the detector 10, and thesecond diode 40 is incorporated in the intermediate stage 16, as shownin FIG. 6. Biased with a constant current, each of the silicon diodes 38and 40 exhibit a temperature dependant voltage that follows changes inthe Fermi level. The Fermi level's temperature dependence produces atemperature dependent potential difference between the n-side conductionband and the p-side conduction band. The temperature dependent voltagechange across a diode, biased with a constant current, is typicallyabout −2.3 mV per degree Kelvin. Utilizing the two diodes 38 and 40,connected back-to-back, as shown in FIG. 6, provides a measure of thetemperature difference between the detector 10 and intermediate stage16. This temperature difference produces an input voltage that isamplified by the amplifier 18, and outputs an output voltage V_(O).

The amplifier 18 in the subject invention includes a bipolar transistorcircuit 42 as shown in FIG. 9 which not only amplifies and provides anoutput signal V_(O), but its quiescent power consumption serves as aheater for the intermediate stage 16, thereby mechanizing theelectrical-thermal feedback loop. This dual function is made possible bydesigning the amplifier circuit 18 including the bipolar transistor 42to operate at equilibrium at a constant current I_(H). Operating theamplifier 18 at a constant current I_(H) insures that the output voltageis not only a measure of the temperature difference between the detector10 and intermediate stages, but also determines the thermal power Q_(H)delivered to the intermediate stage 16. The thermal power Q_(H),delivered by the amplifier 18 to the intermediate stage 16, is simplygiven by:Q _(H) =I _(H) V _(O) =I _(H) A _(G)[2.3mV/K(T _(D) −T _(IN))]  (25)

where, A_(G) is the amplifier's voltage gain and I_(H) is the amplifiersoperating dc bias current. The amplifier's low frequency voltage gain istypically about 10⁵ and I_(H) is about 1 μA. Since I_(H) is heldconstant, as T_(D)>T_(IN) (T_(D)<T_(IN)) V_(O) increases (decreases) theamplifier's quiescent power, causing heating (cooling) of theintermediate stage 16. The intermediate stage's bipolar transistor'stemperature operation (heating and cooling) is made possible byadjusting the temperature of the heat bath 14 to be always lower thatany object in the scene: T_(HB)<{T_(D), T_(IN)}. Thus the combination ofthe amplifier 18 and heat bath 14 provides the desired bipolartemperature operation.

The differential representation of the electrical-thermal feedback isobtain by taking the differential of equation (25) which is expressedas:δQ _(H) =I _(H) A _(G)[2.3mV/K(δT _(D) −δT _(IN))]=A(δT _(D) −δT _(IN)

The electrical-thermal coefficient, A, is readily evaluated by usingA_(G)≈10⁵, I_(H)≈10⁻⁶ amp. Substituting these values into equation (26)we obtain A≈10⁻⁵ W/K, and this is much larger than G₁=G_(1A)+G_(1B) orG₂=G_(1A)+G_(1B) by about 1000 times.

Thus by utilizing three temperature platforms, i.e., the detector 10 atT_(D), intermediate stage 16 at T_(IN), and heat bath 14 at temperatureT_(HB), the thermal electrical feedback adjusts the power Q_(H) appliedto the intermediate stage 16 to make its temperature, T_(IN), convergeto the detector's temperature, T_(D). Minimizing the temperaturedifference between the detector 10 and the intermediate stage 16effectively makes the conductance G₁=G_(1A)+G_(1B) go to zero.

MM USSS AC Response

The AC response is computed from an analysis on a thermal equivalentcircuit of FIGS. 5 and 6 as shown in FIG. 7. The analysis follows anapproach similar to the analysis previously presented for a conventionalbolometer. The analysis implicitly assumes that T_(HB) is always lessthan T_(D) and T_(IN). The analysis demonstrates that electrical-thermalfeedback severely attenuates the conductance of G₁, thereby leading toat least a 25-fold improvement in thermal isolation and increasedresponse. The heat capacity of the detector 10 is represented by C₁ andthe intermediate stage's heat capacity is represented by C₂. Q_(AE)represents the radiation power from the scene delivered through theantenna 20 and coupled to the detector 10. Q_(D) represents theradiation power directly absorbed by the detector 10. Q_(S1) and Q_(S2)represents the radiation power from the radiation shields absorbed bythe detector 10 and the intermediate stage 16. Q_(D1) and Q_(D2)represents the radiation power emitted by the detector 10 and theintermediate stage 16. Q_(H) is the power delivered by theelectrical-thermal feedback circuit.

The thermal balance conditions at the detector 10 and intermediatestages 16 are expressed in terms of two integral equations. At thedetector 10, the equation for thermal balance is given by:

$\begin{matrix}{{Q_{D} + Q_{AE} - Q_{D1} + Q_{S1}} = {{{- {\int_{T_{D}}^{T_{IN}}{{G_{1}(T)}\ {\mathbb{d}T}}}} + {\int_{T_{D}}^{T_{D} + {\delta\; T_{D}}}{j\;\omega\;{C_{1}\left( T_{D} \right)}\ {\mathbb{d}T_{D}}}}}\mspace{230mu} = {{- {\sum\limits_{n = 0}^{\infty}\;\left( {\frac{\partial^{n}{G_{1}\left( T_{D} \right)}}{\partial T_{D}^{n}}\frac{\left( {T_{IN} - T_{D}} \right)^{n + 1}}{\left( {n + 1} \right)!}} \right)}} + {\sum\limits_{n = 0}^{\infty}\;\left( {j\;\omega\frac{\partial^{n}{C_{1}\left( T_{D} \right)}}{\partial T_{D}^{n}}\frac{\left( {\delta\; T_{D}} \right)^{n + 1}}{\left( {n + 1} \right)!}} \right)}}}} & (27)\end{matrix}$

Taking the small temperature change limit, the G₁ and C₁ integrals inEquation 27 are approximated by taking only the Taylor series termslinear with temperature. Using this approximation, and taking thetemperature differential of Equation 27, we obtain a simplifiedexpression which is given by:G _(AE) δT _(SS) +G _(D)δT_(S) =[G ₁ +G _(D1) +jωC _(D) ]δT _(D) −G ₁ δT_(IN)  (28)

From previous discussion, we found G_(AE)δT_(SS)>>G_(D)δT_(S), henceG_(D)δT_(S) can be neglected. Similarly, thermal balance conditions atthe intermediate stage give rise to an integral equation given by:

$\begin{matrix}{{{- Q_{D2}} + Q_{H} + Q_{S2}} = {{{- {\int_{T_{IN}}^{T_{HB}}{{G_{2}(T)}\ {\mathbb{d}T}}}} + {\int_{T_{IN}}^{T_{IN} + {\delta\; T_{IN}}}{j\;\omega\;{C_{2}\left( T_{IN} \right)}\ {\mathbb{d}T_{IN}}}} + {\int_{T_{D}}^{T_{IN}}{{G_{1}(T)}\ {\mathbb{d}T}}}}\mspace{191mu} = {{- {\sum\limits_{n = 0}^{\infty}\;\left( {\frac{\partial^{n}{G_{2}\left( T_{IN} \right)}}{\partial T_{IN}^{n}}\frac{\left( {T_{HB} - T_{IN}} \right)^{n + 1}}{\left( {n + 1} \right)!}} \right)}} + {\sum\limits_{n = 0}^{\infty}\;\left( {j\;\omega\frac{\partial^{n}{C_{2}\left( T_{IN} \right)}}{\partial T_{IN}^{n}}\frac{\left( {\delta\; T_{IN}} \right)^{n + 1}}{\left( {n + 1} \right)!}} \right)} + {\sum\limits_{n = 0}^{\infty}\;\left( {\frac{\partial^{n}{G_{1}\left( T_{D} \right)}}{\partial T_{D}^{n}}\frac{\left( {T_{IN} - T_{D}} \right)^{n + 1}}{\left( {n + 1} \right)!}} \right)}}}} & (29)\end{matrix}$

As in Equation 27, taking the small temperature change limit, theintegrals for G₁, G₂, and C₂ are approximated by only the Taylor seriesterms linear in temperature. Taking the temperature differential ofEquation 29 and combining with Equations 26 and 16, we obtain asimplified expression which is given by:[G ₁ +A]δ _(D) =[G ₁ +G ₂ +G _(D2) +A+jωC ₂ ]δT _(IN)  (30)

Since A>>{G₁, G₂, G_(D2)}, it becomes evident from Equation 30 that theelectrical-thermal feedback forces δT_(D)≈T_(IN). Under such conditionsthe thermal current through G₁ is not changed even though thetemperature T_(D) of the detector 10 changes. The improvement in thermalisolation is explicitly revealed combining Equations 29 and 30 toeliminating T_(IN). Combining Equations 29 and 30 to eliminate T_(IN),after some rearrangements we obtain an expression for T_(D) as afunction of T_(SS), specifically:

$\begin{matrix}{{\delta\; T_{D}} = {{\frac{G_{AE}}{\left\lbrack {G_{D1} + {j\;\omega\; C_{1}} + \frac{G_{1}\left\lbrack {G_{2} + G_{D2} + {j\;\omega\; C_{2}}} \right\rbrack}{\left\lbrack {G_{1} + G_{2} + G_{D2} + A + {j\;\omega\; C_{2}}} \right\rbrack}} \right\rbrack}\delta\; T_{SS}} \cong {\frac{\left\lbrack \frac{G_{AE}}{G_{D1}} \right\rbrack}{\left\lbrack {1 + \frac{j\;\omega\; C_{1}}{G_{D1}}} \right\rbrack}\delta\; T_{SS}}}} & (31)\end{matrix}$

Equation 31 reveals that for large thermal electrical feedback values,A>>{G₁, G₂, G_(D2)}, the change in radiometric scene temperature δT_(SS)is related to δT_(D) by an approximation represented by the right side,of Equation 31. This comes about because the temperature of theintermediate stage 16 of T_(IN) tracks change in the temperature of thedetector 10, effectively making the thermal conductance of G₁ seem muchsmaller. Except for limits imposed by noise, the thermal conductance G₁should approach zero as A goes to infinity.

For the values used here, A≈10⁻⁵ W/K (see Equation 26) is much largerthan the typical values of 10G₁G₂≈10⁻⁷W/K. Therefore, actions of thethermal electrical feedback reduces conductance G₁≈40G_(D1), below theconductance G_(D1). This reduction leads directly to at least a 40-foldresponse increase, as evident from comparing the denominators inEquations 3 and 31. The increased response is evident from the change inthe detector's temperature δT_(D) in response to a change in radiometricscene temperature δT_(SS)(see Equation 31). The increased responsivityproduces an important benefit, since it provides signals much improvedto corruptions by various noise sources, thereby leading directly toimproved sensitivity.

The AC temperature response of the detector 10, given by theapproximation in Equation 31, is according to the time constantC₁/G_(D1). For TV frame rates, this requires the heat capacity of thedetector 10 be minimized. With the antenna 20 as shown in FIG. 5, thesize of the detector can be minimized without affecting significantlythe MM wave signal. In particular, the size of the detector 10 inaccordance with a preferred embodiment of the subject invention as shownin FIG. 5, will be about 5 μM in diameter, much smaller that theanticipated size of the pixel 9, about 1000 μM square. This approach isviable to realizing a time constant consistent with TV frame rates,e.g., 0.167 seconds.

With the interrelationships between δT_(D), δT_(IN), and δT_(SS), givenby Equations 30 and 31, we will now proceed to compute the MM USSSvoltage response. The power Q_(H), delivered by the electrical-thermalfeedback amplifier 18 provides the output signal V_(O). Changes in thepower δQ_(H) delivered by the electrical-thermal feedback circuit isrelated simply to the output signal δV_(O) by the bias current I_(H),since δQ_(H)=−δV_(O)I_(H), see Equation (26). Incorporating thisrelationship into Equation 30, and after some rearrangement, we obtainan expression for the output signal dependence on δT_(D), δT_(IN), whichis given as:δV _(O) I _(H) =G ₁ δT _(D) −[G ₁ +G ₂ +G _(D2) +jωC ₂ ]δT _(IN)  (32)

Voltage responsivity is obtained by eliminating δT_(IN) and δT_(D) byreplacing them with δT_(SS). The replacement is accomplished in twosteps. First, using Equation (30), we replace δT_(IN) by δT_(D). Second,using Equation (31), we replace δT_(D) by δT_(SS). Performing all thesesubstitutions, and after some rearrangements, the MM USSS responsivityis expressed by:

$\begin{matrix}{\frac{\delta\;{V_{O}(\omega)}}{\delta\;{T_{SS}(\omega)}} = {\frac{A\frac{G_{AE}}{I_{H}}}{{\left\lbrack {1 + \frac{\left( {G_{1} + A} \right)}{\left( {G_{2} + G_{D2} + {j\;\omega\; C_{2}}} \right)}} \right\rbrack\left( {G_{D1} + {j\;\omega\; C_{1}}} \right)} + G_{1}}\mspace{85mu} \approx {\left( \frac{G_{2} + G_{D2}}{I_{H}} \right)\left( \frac{G_{AE}}{G_{D1}} \right)\frac{\left\lbrack {1 + {j\frac{\omega\; C_{2}}{G_{2} + G_{D2}}}} \right\rbrack}{\left\lbrack {1 + {j\frac{\omega\; C_{1}}{G_{D1}}}} \right\rbrack}{Volts}\text{/}{Kelvin}}}} & (33)\end{matrix}$

The approximations for Equation 33 are made possible by using the factthat A>>{G₁, G₂, G_(D2)}. Several features become evident by examiningEquation (33). The output voltage V_(O) is a product of two factors andtwo time constants.

The first factor reveals that the voltage responsivity increases withhigher thermal conductance G₂ and lower bias current I_(H). This occursbecause for a given change in radiometric scene temperature δT_(SS) thepower that the amplifier 18 has to deliver to the intermediate stage 16increases with higher thermal conductance G₂. Since I_(H) is fixed, theonly way the amplifier 18 can deliver more power is by increasing theoutput voltage V_(O). Hence it appears as though the voltageresponsivity has increased, at the cost of more power consumption pereach pixel, and or higher dc operating voltage.

Similarly, the voltage responsivity varies inversely with I_(H) Because,for a given change in radiometric scene temperature δT_(SS) and aconstant thermal conductance G₂, the power that the amplifier 18 has todeliver to the intermediate stage 16 remains constant. As we decreaseI_(H) the amplifiers output voltage needs to increase to keep constantthe power delivered.

The two time constants in Equation (33) are a pole, representing thetime constant of the detector 10, and a zero, representing time constantof the intermediate stage 16. The time constant of the detector 10 willcase the voltage responsivity to decrease. If the detector 10 had zeroheat capacity, (C₁=0) the rise in the detector's temperature wouldcorrespond to the radiation power supplied divided by the thermalloading on the detector, given as G_(D1). However, before the detectorstemperature can change, the detector's heat capacity, C₁, need toreceive (it T_(D) increases) or release (if T_(D) decreases) energy andthis delay manifest itself as a decrease in the ac voltage response.

The second time constant in Equation (33) represents the time constantof the intermediate stage 16. This time constant has the opposite effectto the detector's time constant: it increases the voltage responsivity.This can be understood by examining the operation of theelectrical-feedback circuit. If the heat capacity of the intermediatestage 16 is zero, C₂=0, the temperature rise of the intermediate stageis simply the output power provided by the electrical-feedback circuit(or V_(O)I_(H)) divided by the thermal loading (G₂+G_(D2)). However,since the heat capacity C₂≠0, more (less) power need to be supplied tothe intermediate stage 16 for an increase (decrease) in detector'stemperature. Hence it follows that the amplifiers output voltage of theamplifier 18 will be larger (smaller) if the intermediate stagetemperature needs to increase (decrease) to converge to the detector'stemperature T_(D).

In principle and to first order, the two time constants can be used toextend the frequency response of the MM USSS beyond the detector's timeconstant. This can be achieved by making the time constant of theintermediate stage 16 equal to the time constant of the detector 10.

Noise Level in MM USSS

The noise sources in the MM USSS of the present invention are all thenoise sources present in conventional bolometers; however, additionalnoise is produced by the electrical-thermal feedback output power Q_(H).Specifically, the radiation induced thermal fluctuations noises include:scene's flux Q_(S); radiation shields' Q_(S1) and Q_(S2); the bolometerQ_(D1) of the detector 10; and the Q_(D2) of the intermediate stage 16.We also include thermal fluctuations from the heat bath 14 coupled intothe detector 10 through conductance G₁=G_(1A)+G_(1B) andG₂=G_(2A)+G_(2B). Finally we include the noise from theelectrical-thermal feedback loop. All these noise sources inducetemperature fluctuations in the detector's temperature,indistinguishable from a signal. Since the MM USSS output is a voltagesignal V_(O), all the noise terms are itemized and given as a noisevoltage.

Specifically, the MM USSS noise is given as RMS voltage fluctuationsproduced by temperature fluctuations in: (1) the scene, δV_(O)(T_(SS)),(2) the heat bath 10, δV_(O)(T_(HB)), (3) the detector 10 stage'stemperature δV_(O)(T_(D)), and (4) the intermediate stage's 16temperature δV_(O)(T_(IN)). Additionally, fifth noise term is from theelectrical-thermal feedback and readout circuits contained in each MMUSSS pixel δV_(O)(E_(L)). An expression for each one of these noisecomponents is derived and given below.

The overall noise is computed by utilizing the transfer function betweenthe various noise sources and the detector output. We make use of ourknowledge of the RMS value of the fluctuations in: radiometrictemperature T_(SS), the heat bath temperature T_(HB), the detector stagetemperature stage T_(D), the intermediate stage temperature T_(IN), andthe readout electronics. Each RMS value is treated as a standarddeviation obtained from a Fourier representation of a particular noisefluctuation. Using the principle of superposition, we use the differenttransfer function, summed over all frequencies, to compute thecontribution of each noise source to the detector's output.

(I.) Fluctuations in the radiometric scene temperature, δT_(SS),contributes noise to the MM USSS output δV_(O)(T_(SS)), and the transferfunction for this contribution is given by Equation (33). For maximumfrequency response, we would adjust he pole and zero in Equation (33) tocancel. The noise contribution from spectral fluctuations δT_(SS)(ω) inradiometric scene temperature to fluctuations in the detector's outputare approximately given as:

$\begin{matrix}{{\delta\;{V_{O}\left( {T_{SS}(\omega)} \right)}} \cong {{\left\lbrack \frac{G_{2} + G_{D2}}{I_{H}} \right\rbrack\left\lbrack \frac{G_{AE}}{G_{D1}} \right\rbrack}\delta\;{T_{SS}(\omega)}}} & (34)\end{matrix}$

Integrating these contributions over frequency, we obtain the corruptionof the detector's output voltage due to RMS fluctuations in the scenetemperature δT_(SS)(RMS) and it is given by:

$\begin{matrix}{{\delta\;{V_{O}\left( T_{SS} \right)}} \cong {{\left\lbrack \frac{G_{2} + G_{D2}}{G_{D1}} \right\rbrack\left\lbrack \frac{G_{AE}}{I_{H}} \right\rbrack}\delta\;{T_{SS}({RMS})}}} & (35)\end{matrix}$

Thermal conductance ratios at the detector represented by the ratioG_(AE)/G_(D1)≈0.5 reduces the noise from the scene. However, the signalis also reduced by the same amount thereby increasing susceptibility tocorruption by the other noise sources and decreasing the sensitivity.

(II.) Temperature [δT_(HB)(RMS)] fluctuations of the heat bath 14produce fluctuations in the output signal of the detector 10. Thiscontribution is calculated by using the fact that according to Equation26 δQ_(H)=I_(H)δV_(O)=A[δT_(D)−δT_(IN)]. Thus, by calculating the changeproduced by δT_(HB)(RMS) on δT_(D) and δT_(IN) we obtain δV_(O)(T_(HB))with Equation 26. Using superposition, and under the conditions thatδT_(HB)≠0 and δT_(SS)=δT_(S)=0, we take the differentials of Equations27 and 29 and obtain the influence of fluctuations in δT_(HB)(ω) onδT_(D)(ω) and δT_(IN)(ω). Spectral representation is used since weintend to sum the different Fourier noise terms to obtain the RMS value.Taking the differential of Equation 27, and after rearranging tosimplify, we obtain:[G _(S1) +jωC _(HB) ]δT _(HB)(ω)+[G ₁ ]δT _(IN)(ω)=[G ₁ +G _(D1) +jωC ₁]δT _(D)(ω)  (36)

Repeating the same procedure for Equation 29, we obtain a secondequation for the interrelation between the noise terms, and it is givenby:[G ₂ +G _(S2) +jωC _(HB) ]δT _(HB)(ω)+[G ₁ +A]δT _(D)(ω)=[G ₁ +G ₂ G_(D2) +A+jωC ₂ ]δT _(IN)(ω)  (37)

In Equation 37, we used the fact that δQ_(H)=A[δT_(D)−δT_(IN)]. Solvingequations 36 and 37 for δT_(D)(ω) and δT_(IN)(ω) in terms of δT_(HB)(ω),we compute the spectral variations in the output voltage δV_(O)(ω) ofthe amplifier 18 due to the heat bath 14 as:

$\begin{matrix}{{{\delta\;{V_{O}(\omega)}} = {{\frac{A}{I_{H}}\left\lbrack \frac{\left( {G_{S1} + {j\;\omega\; C_{HB}}} \right) - {\left( {G_{D1} + {j\;\omega\; C_{1}}} \right)\frac{\left( {G_{2} + G_{S2} + {j\;\omega\; C_{HB}}} \right)}{\left( {G_{2} + G_{D2} + {j\;\omega\; C_{2}}} \right)}}}{\left( {G_{1} + G_{D1} + {j\;\omega\; C_{1}}} \right) + {\left( {G_{1} + A} \right)\frac{\left( {G_{D1} + {j\;\omega\; C_{1}}} \right)}{\left( {G_{2} + G_{D2} + {j\;\omega\; C_{2}}} \right)}}} \right\rbrack}\delta\;{T_{HB}(\omega)}}}\;} & (38)\end{matrix}$

This equation is simplified by recognizing that the bath's heat capacityC_(HB) is arbitrarily large. Incorporating this into Equation 38 withthe fact that a is very large, we approximate and obtain a simplifiedexpression and it is given by:

$\begin{matrix}{{\delta\;{V_{O}(\omega)}} = {\left\lbrack \frac{G_{2}}{I_{H}} \right\rbrack\frac{j\;\omega\; C_{HB}}{\left\lbrack \left( {G_{D1} + {j\;\omega\; C_{1}}} \right) \right\rbrack}\delta\;{T_{HB}(\omega)}}} & (39)\end{matrix}$

The RMS noise produced by the thermal fluctuations in the heat bath 14is obtained by using the power spectral density of a thermal body (terminside the integral and the square bracket in Equation 40). ConvertingEquation 39 into a power spectral density integral, the expression forthe output noise voltage produced by the heat bath temperature becomes:

$\begin{matrix}{{\delta\;{V_{O}\left( T_{HB} \right)}} \approx {\frac{G_{2}}{I_{H}}\sqrt{\int_{0}^{\infty}{\frac{\omega^{2}{C_{HB}^{2}\left\lbrack \frac{4\; G_{D1}{kT}_{HB}^{2}}{G_{D1}^{2} + {\omega^{2}C_{HB}^{2}}} \right\rbrack}}{{\left( {G_{D1} + {j\;\omega\; C_{1}}} \right)}^{2}}\ \frac{\mathbb{d}\omega}{2\pi}}}}} & (40)\end{matrix}$

Equation 38 can be simplified by recognizing several conditions. Theratio G₁/C_(HB) is very small, leading to factorization of the ω²C_(HB)² terms inside the integral. Incorporating these approximations andintegrating over frequency, we obtain a simple relationship given by:

$\begin{matrix}{{\delta\;{V_{O}\left( T_{HB} \right)}} \cong {\left\lbrack \frac{G_{2}}{I_{H}} \right\rbrack\left\lbrack \frac{{kT}_{HB}^{2}}{C_{1}} \right\rbrack}^{1/2}} & (41)\end{matrix}$

This represents the RMS fluctuations in the output voltage of theamplifier 18 due to fluctuations in the temperature of the heat bath 14.The level is the minimum thermodynamic noise level possible andsurprisingly is independent of the heat capacity of the heat bath 14 anddependent on the heat capacity of the detector 10.

(III.) Fluctuations in the temperature T_(D) of the detector 10 willincrease the fluctuations in the output noise voltage. Using theequivalent circuit in FIG. 6, we sum the power at node T_(D), whenδQ_(IN)=δQ_(H)=0, and obtain the following expression:δQ _(D)(ω)=(G ₁ +G _(D1) +jωC ₁)δT _(D)(ω)−G ₁ δT _(IN)(ω)  (42)

Using Equation 28, we eliminate the variable δT_(IN) from Equation 42and obtain the following expression:

$\begin{matrix}{{\delta\;{Q_{D}(\omega)}} = {\left\lbrack {G_{D1} + {j\;\omega\; C_{1}} + \frac{G_{1}\left( {G_{2} + G_{D2} + {j\;\omega\; C_{2}}} \right)}{\left( {G_{1} + G_{2} + G_{D2} + A + {j\;\omega\; C_{2}}} \right)}} \right\rbrack\delta\;{T_{D}(\omega)}}} & (43)\end{matrix}$

From previous computations with Equation 26, we obtain an expression forthe noise voltage produced by temperature fluctuations in T_(D), and itis given by:

$\begin{matrix}\begin{matrix}{{\delta\;{V_{O}\left\lbrack {T_{D}(\omega)} \right\rbrack}I_{H}} = {{A\left\lbrack {1 - \frac{\delta\; T_{IN}}{\delta\; T_{D}}} \right\rbrack}\delta\; T_{D}}} \\{= {{A\left\lbrack \frac{G_{2} + G_{D2} + {j\;\omega\; C_{2}}}{G_{1} + G_{2} + G_{D2} + A + {j\;\omega\; C_{2}}} \right\rbrack}\delta\;{T_{D}(\omega)}}}\end{matrix} & (44)\end{matrix}$

Combining Equation 44 with Equation 43, we obtain an analytical solutionfor the spectral noise dependence due to fluctuations in the powerδQ_(D), and it is given by:

$\begin{matrix}{{\delta\;{V_{O}\left\lbrack {T_{D}(\omega)} \right\rbrack}I_{H}} = \frac{A\;\delta\;{Q_{D}(\omega)}}{{\left\lbrack {1 + \frac{\left( {1 + A} \right)}{\left( {G_{2} + G_{D2} + {{j\omega}\; C_{2}}} \right)}} \right\rbrack\left( {G_{D1} + {{j\omega}\; C_{1}}} \right)} + G_{1}}} & (45)\end{matrix}$

The power spectral density square of δQ_(D) is given asd²Q_(D)/df=4G_(D1)k_(B)(T_(D))², and combining this with the absolutesquare of equation 45, integrating and taking the square root we obtainthe RMS voltage fluctuations in δV_(O)(T_(D)), produced by T_(D).Performing these operations, with some simplifications, we obtain:

$\begin{matrix}{{\delta\;{V_{O}\left( T_{D} \right)}} = {\frac{G_{2}^{*} + G_{D2}}{I_{H}}\left\lbrack \frac{k_{B}T_{D}}{C_{1}} \right\rbrack}^{1/2}} & (46)\end{matrix}$

(IV.) Contributions from noise fluctuations in δT_(IN)(ω) to the outputsignal of the amplifier 18 are calculated similarly to contributionsfrom δT_(D)(ω). Using the equivalent circuit in FIG. 8, we sum the powerat node T_(D), when δQ_(D)=δQ_(H)=0, and obtain a relationship betweenδT_(D)(ω) and δT_(IN)(ω) given by:

$\begin{matrix}{{\delta\;{T_{D}(\omega)}} = {\left\lbrack \frac{G_{1}}{\left( {G_{1} + G_{D1} + {{j\omega}\; C_{1}}} \right)} \right\rbrack\delta\;{T_{IN}(\omega)}}} & (47)\end{matrix}$

Since we are calculating the effect of noise source δQ_(IN), thetemperature fluctuations δT_(IN)(ω) in Equation 47 shows that|T_(IN)|>|T_(D)|. Summing the power at node T_(IN) in FIG. 8, we obtaina spectral power relationship given by:δQ _(IN)(ω)+δQ _(H)(ω)=[G₁ +G ₂ +G _(D2) +jωC ₂ ]δT _(IN)(ω)−G ₁ δT_(D)(ω)  (48)

Using the fact that δQ_(H)=A[δT_(D)−δT_(IN)], and Equation 47, wereplace eliminate variable δQ_(H) and δT_(D) in Equation 48 and obtain:

$\begin{matrix}{{\delta\;{Q_{IN}(\omega)}} = {\left\lbrack {\left( {G_{2} + G_{D2} + {{j\omega}\; C_{2}}} \right) + \frac{\left( {A + G_{1}} \right)\left( {G_{D1} + {{j\omega}\; C_{1}}} \right)}{\left( {G_{1} + G_{D1} + {{j\omega}\; C_{1}}} \right)}} \right\rbrack\delta\;{T_{IN}(\omega)}}} & (49)\end{matrix}$

Using Equation 26, we obtain an expression for the spectral fluctuationsin the output voltage V_(O)[T_(IN)(ω)] produced by thermal fluctuationsat node T_(IN) and it is given by:

$\begin{matrix}\begin{matrix}{{\delta\;{V_{O}\left\lbrack {T_{IN}(\omega)} \right\rbrack}I_{H}} = {{- {A\left\lbrack {1 - \frac{\delta\; T_{D}}{\delta\; T_{IN}}} \right\rbrack}}\delta\; T_{IN}}} \\{= {{- {A\left\lbrack \frac{G_{D1} + {{j\omega}\; C_{1}}}{G_{1} + G_{D1} + {{j\omega}\; C_{1}}} \right\rbrack}}\delta\;{T_{IN}(\omega)}}}\end{matrix} & (50)\end{matrix}$

Combining Equations 49 and 50, to eliminate δT_(IN)(ω), we obtain anexpression for the spectral voltage fluctuations at node T_(IN) in termsof the spectral fluctuations in the black body radiation and this isgiven by:

$\begin{matrix}{{\delta\;{V_{O}\left\lbrack {T_{IN}(\omega)} \right\rbrack}I_{H}} = \frac{\delta\;{Q_{IN}(\omega)}}{\left\lbrack {1 + \frac{G_{1}}{A} + \frac{\left( {G_{2} + G_{D2} + {{j\omega}\; C_{2}}} \right)\left( {G_{1} + G_{D1} + {{j\omega}\; C_{1}}} \right)}{A\left( {G_{D1} + {{j\omega}\; C_{1}}} \right)}} \right\rbrack}} & (51)\end{matrix}$

Since A is very large, Equation 51 reveals that the power associatedwith the spectral voltage fluctuations equals to the power in the powerfluctuations in the black body radiation, regardless of the thermalelectrical feedback loop. The power fluctuations at node T_(IN)correspond to the classical temperature variance at T_(IN) times thethermal conductivity from this node to the surroundings. Thus the RMS involtage V_(O), due to the thermal fluctuations at node T_(IN), is givenas:

$\begin{matrix}{{\delta\;{V_{O}\left\lbrack T_{IN} \right\rbrack}} = {\frac{G_{2} + G_{D2}}{I_{H}}\left\lbrack \frac{{kT}_{IN}^{2}}{C_{2}} \right\rbrack}^{1/2}} & (52)\end{matrix}$

With Equation 52, we complete calculating all the RMS contributions tothe output voltage V_(O) of the amplifier 18 produced by temperaturefluctuations in T_(HB), T_(S), T_(D) and T_(IN). The remaining noisecontribution is from the thermal electrical feedback circuit and this iscomputed below.

(V.) The noise from the readout and thermal electrical feedback circuitof the preferred embodiment of the invention shown in FIG. 9, includingthe bipolar transistor 42, contribute noise to the output signal asfollows. This contribution is computed with the aid of the equivalentcircuit of FIG. 9 shown in FIG. 10. For convenience, all the electricalnoise terms have been included into the current generator labeledI_(N0). This represents the noise present without any form of feedback.Additionally, this analysis is based on the fact that the noise in thecircuit can be represented in terms of a Fourier representation withcoefficients I_(N0). Doing the analysis for an arbitrary frequency withamplitude I_(N0), provides us with the expression for the noise withelectrical thermal feedback.

The noise flowing in the circuit is affected by the electrical andelectrical-thermal feedback present in the readout circuit shown in FIG.9. Thus the current noise level without any feedback, INO, (FIG. 10) ismodified to a new level in when feedback effects are included and it isgiven by:I _(N0)(ω)+[g _(m) +G _(m) ][δV _(B)(ω)−δV _(O)(ω)]=I _(N)(ω)  (53)

Where g_(M) is the bipolar transistors' transconductance and 1/G_(M) isthe diode's impedance. The voltage difference between base and emitterhas an ac component and a thermal component, because the Fermi levelstemperature dependence in the ‘p” and “n” regions of the diode andbipolar transistor. Accordingly, the base-emitter voltage difference forthe bipolar transistor is given as:

$\begin{matrix}{{{V_{B}(\omega)} - {V_{O}(\omega)}} = {{\delta\;{V_{O}(\omega)}\left( {\frac{Z_{1}}{Z_{1} + {1/g_{m}}} - 1} \right)} + {\frac{\partial V_{BE}}{\partial T}\left( {{\delta\; T_{D}} - {\delta\; T_{IN}}} \right)}}} & (54)\end{matrix}$

The first term on the right of Equation 54 represents the electricaldivision of the output voltage by the diode 38 in series with impedanceZ₁, under the assumption that the base current is very small. The secondterm on the right of Equation 54 represents the change in the thermalvoltage produced by temperature changes in the diode (T_(D)) andtransistor (T_(IN)) temperatures. The coefficient ∂V_(BE)/∂T representhow change in the voltage per degree Kelvin, and typically,∂V_(BE)/∂T≅−2.3 MV/K. The change in the output voltage δV_(O)(ω) isreadily computed by including all the impedances at the output node andthe actual noise current flowing, feedback effects included, and this isgiven by:

$\begin{matrix}{{\delta\;{V_{O}(\omega)}} = {\left( \frac{\left( {{1/g_{m}} + Z_{1}} \right)Z_{OO}}{{1/g_{m}} + Z_{1} + Z_{OO}} \right){I_{N}(\omega)}}} & (55)\end{matrix}$

Incorporating Equation 55 into Equation 54, and after rearranging someterms, we obtain a better representation for Equation 53, and it isgiven by:

$\begin{matrix}{{I_{NO}(\omega)} = {{{I_{N}(\omega)}\left\lbrack {1 + \frac{\left( {G_{m} + g_{m}} \right)Z_{OO}}{1 + {g_{m}\left( {Z_{1} + Z_{OO}} \right)}}} \right\rbrack} - {\left( {g_{m} + G_{m}} \right)\frac{\partial V_{BE}}{\partial T}\left( {{\delta\; T_{D}} - {\delta\; T_{IN}}} \right)}}} & (56)\end{matrix}$

Observing Equation 56, it is evident that current I_(N) is smaller thatthe original noise current I_(N0) provided the thermal term in Equation56 is positive, when expressed in terms of I_(N). In fact, it willbecome evident that the electrical-thermal feedback term further reducesthe noise current, and this is computed below.

Taking Equation 48 under the conditions that δQ_(IN)(ω)=0, we obtain arelationship between I_(N)(ω), δT_(D)(ω), and δT_(IN)(ω) and it is givenas:−I _(H) δV _(O)(ω)=(G ₁ +G ₂ +G _(D2) +jωC ₂)δT _(IN)(ω)−G ₁ δT_(D)(ω)  (57)

We have included a term −I_(H)δV_(O)(ω)=δQ_(H)(ω), and it representchanges in power consumed at the intermediate stage caused by a changein the output voltage δV_(O)(ω) for dc current I_(H) flowing into theoutput node. As the noise current increases, the output voltagedecreases, and the quiescent power consumed by the intermediate stagealso decreases, hence the minus sign on the left side of Equation 57.Earlier in Equation 47 we expressed a relationship between δT_(D)(ω) andδT_(IN)(ω).

Combining Equations 57 and 47, we eliminate δT_(D)(ω), and obtainδT_(IN)(ω) as a function of I_(H)V_(O)(ω), and it is given by

$\begin{matrix}{{\delta\;{T_{IN}(\omega)}} = \frac{{- I_{H}}\delta\;{V_{O}(\omega)}\left( {G_{1} + G_{D1} + {{j\omega}\; C_{1}}} \right)}{{\left( {G_{1} + G_{D1} + {{j\omega}\; C_{1}}} \right)\left( {G_{2} + G_{D2} + {{j\omega}\; C_{2}}} \right)} + {G_{1}\left( {G_{D1} + {{j\omega}\; C_{1}}} \right)}}} & (58)\end{matrix}$

The right most term in Equation 56 is expressed in terms of I_(N)(ω) byreplacing δT_(D)(ω) with Equation 47, and δT_(IN)(ω) with Equation 58,and δV_(O)(ω) with Equation 55. Performing all these substitutions andafter some rearranging, we obtain an expression for I_(N0)(ω) in termsof I_(N)(ω) which is:

$\begin{matrix}{{I_{N0}(\omega)} = {{I_{N}(\omega)}\left\{ {1 + \frac{\left( {g_{m} + G_{m}} \right)Z_{00}}{1 + {g_{m}\left( {Z_{1} + Z_{00}} \right)}} - \frac{\left( {g_{m} + G_{m}} \right)I_{H}\frac{\partial V_{BE}}{\partial T}\frac{\left( {1 + {g_{m}Z_{1}}} \right)Z_{00}}{1 + {g_{m}\left( {Z_{1} + Z_{00}} \right)}}}{\left\lbrack {G_{1} + \frac{\left( {G_{1} + G_{D1} + {{j\omega}\; C_{1}}} \right)\left( {G_{2} + G_{D2} + {{j\omega}\; C_{2}}} \right)}{\left( {G_{D1} + {{j\omega}\; C_{1}}} \right)}} \right\rbrack}} \right\}}} & (59)\end{matrix}$

The output noise voltage due to the readout and electrical-thermalfeedback circuit is readily obtained by combining Equations 55 and 59 toobtain:

$\begin{matrix}{{\delta\;{V_{O}(\omega)}} = \frac{I_{N0}(\omega)}{\begin{matrix}\left\{ {\frac{1 + {g_{m}Z_{1}} + {\left( {{2g_{m}} + G_{m}} \right)Z_{00}}}{\left( {1 + {g_{m}Z_{1}}} \right)Z_{00}} -} \right. \\\left. \frac{\left( {g_{m} + G_{m}} \right)I_{H}\frac{\partial V_{BE}}{\partial T}}{\left\lbrack {G_{1} + \frac{\left( {G_{1} + G_{D1} + {{j\omega}\; C_{1}}} \right)\left( {G_{2} + G_{D2} + {{j\omega}\; C_{2}}} \right)}{\left( {G_{D1} + {{j\omega}\; C_{1}}} \right)}} \right\rbrack} \right\}\end{matrix}}} & (60)\end{matrix}$

There are two terms in the denominator that influence the output noisevoltage: an electrical feedback term and a thermal feedback term. Thevalue of ∂V_(BE)/∂T≅−2.3 MV/K is negative thereby removing the negativesign from the thermal term in the denominator. The issue is how large isthe denominator in Equation 60, since the denominator determines howmuch the noise current gets attenuated by electrical and thermalfeedback effects. The amount of attenuation is estimated by recognizingthat Z₁≅Z₀₀ and 10g_(M)≈G_(M), and that the thermal term is much smallerthan the electrical term in the denominator of Equation 60.Incorporating these, Equation 60 is simplified to:

$\begin{matrix}{{\delta\;{V_{O}(\omega)}} = {\frac{I_{N0}(\omega)}{\left\lbrack {{\frac{1}{Z_{1}}\frac{G_{m}}{g_{m}}} + \frac{1}{Z_{00}}} \right\rbrack} \cong {{I_{N0}(\omega)}Z_{1}\frac{g_{m}}{G_{M}}}}} & (61)\end{matrix}$

It should be noted that the smaller the ratio of g_(M)/G_(M) is the morethe noise is attenuated. This feature and the value of impedance Z₁ areused to minimize the noise from the readout and electrical-thermalfeedback circuit. In our example, the ratio is ten to one, leading to aten fold reduction in the electronic circuit noise.

The RMS output noise voltage is evaluated by utilizing Equation 61 andthe noise power spectral density. A general expression for the noisepower spectral density is given as:

$\begin{matrix}{\frac{\mathbb{d}^{2}{I_{N0}(\omega)}}{\mathbb{d}f} = {I_{NO}^{2}\left\lbrack {1 + \frac{B}{f}} \right\rbrack}} & (62)\end{matrix}$

The noise power spectral density includes white noise and 1/f noise. Thewhite noise power spectral density amplitude is given by a constant[I_(N0)]² and the 1/f noise corner frequency is represented by theconstant B. For bipolar transistors, such as the transistor 42 shown inFIG. 9, the value of B is estimated to be about 1.0 KHz and could be aslow as 100 Hz. The expression for the impedance Z₁ corresponds to aparallel combination of a resistance R₁₀ and capacitance C₁₀, and isgiven as Z₁=R₁₀/(1+jωR₁₀C₁₀). Combining all these terms, the equationfor the RMS value for the noise voltage is given by:

$\begin{matrix}{{\delta\;{V_{O}({RMS})}} = {\frac{g_{m}}{G_{m}}I_{N0}R_{10}\sqrt{\left\lbrack {\frac{1}{2\pi}{\int_{0}^{\infty}\frac{\mathbb{d}w}{1 + {R_{10}^{2}C_{10}^{2}\omega^{2}}}}} \right\rbrack + \left\lbrack {\frac{1}{2\pi}{\int_{\omega_{1}}^{\infty}\frac{B{\mathbb{d}\omega}}{\omega\left( {1 + {R_{10}^{2}C_{10}^{2}\omega^{2}}} \right)}}} \right\rbrack}}} & (63)\end{matrix}$

The absolute value squared is used for the impedance Z₁ because thecalculation deals with RMS value of the noise. Additionally, the 1/fnoise term is integrated not from zero do avoid divergence. Instead weselected a radial frequency ω₁ which is connected to system calibration.Performing the integration on Equation 63 we obtain a closed form valuefor the electronic noise and it is given as:

$\begin{matrix}{{\delta\;{V_{O}({RMS})}} = {\frac{g_{m}}{G_{m}}I_{N0}R_{10}\sqrt{\frac{1}{4R_{10}C_{10}} - {\frac{B}{\pi}{{Ln}\left\lbrack {\omega_{1}R_{10}C_{10}} \right\rbrack}}}}} & (64)\end{matrix}$

The value of the RMS circuit noise voltage will be compared against thevalue of the noise voltages from thermal sources. Ideally, we shouldminimize the circuit voltage to achieve optimum performance.

Total Noise Voltage at MM Ultra Sensitive Silicon Sensor

The total noise at the output of the bolometer pixel 9 (FIG. 9) is theRMS sum of the results given in Equations 35, 41, 46, 52 and 64.Combining all these Equations, the expression for the total RMS noisevoltage at the pixel's output is given by:

$\begin{matrix}{{\delta\;{V_{O}({RMS})}} \geq {\frac{G_{2}}{I_{H}}\begin{bmatrix}{{\left( \frac{G_{AE}}{G_{D1}} \right)^{2}\delta\; T_{SS}^{2}} + \left( \frac{{kT}_{HB}^{2}}{C_{1}} \right) + \left( \frac{{kT}_{D}^{2}}{C_{1}} \right) + \left( \frac{{kT}_{IN}^{2}}{C_{2}} \right) +} \\{\left( {\frac{1}{4R_{10}C_{10}} - {\frac{B}{\pi}{{Ln}\left\lbrack {\omega_{1}R_{10}C_{10}} \right\rbrack}}} \right)\left( {I_{N0}R_{10}\frac{g_{m}}{G_{m}}\frac{I_{H}}{G_{2}}} \right)^{2}}\end{bmatrix}}^{1/2}} & (65)\end{matrix}$

The expression for the total RMS voltage noise includes contributionsfrom: the scene, the heat bath 14, the detector 10, the intermediatestage 16, and the readout electronics including the bipolar transistor18.

Several things are evident from Equation 65. Similar to the signal (seeEquation 33), the noise from the scene signal (represented by the firstterm in the square brackets in Equation 65) is attenuated byG_(AE)/G_(D)≈1/30. This attenuation makes all the other noise sourcesmore significant and degrades sensitivity. The second term in the squarebrackets represents the noise from the heat bath 14, and can be reducedby making T_(HB) of the heat bath less than T_(S). of the scene. Thethird term in the square brackets represents the noise from the detector10 and the fourth term represent the noise term from the intermediatestage 16. The noise from the intermediate stage 16 can be minimized bymaking C₁<<C₂, while the thermal electrical feedback insures thatT_(D)≈T_(IN). The last term represents the electronic readout noise. Forbest performance, the electronic noise should be less than the thermalnoise terms associated with the MM USSS. Specifically, the terms in thesquare brackets in Equation 65, given by (KT_(D) ²/C₁), that isapproximately equal to (KT_(HB) ²/C₁), since T_(HB)≈T_(D). The value ofthis term can be readily estimated by recognizing that T_(D)≈300K. Thedetector's heat capacity C₁ is estimated to be equal C₁≅1.56×10⁻¹¹ J/K,corresponding to the heat capacity of a 5 μm diameter silicon membrane0.5 μm thick, and K=1.38×10⁻²³J/K. Combining all these terms, the valuecalculated for (KT_(D) ²/C₁)≅8×10⁻⁸ K². The ultimate sensitivity isachieved when the leading term in the square brackets is larger than allthe other terms. Given that the ration G_(AE)/G_(D1)1/30, we concludethat the sensor is limited by the RMS sum of its own thermalfluctuations {second third an forth terms in the square bracket ofEquation 65} and the value of the electronic readout noise, fifth termin the square brackets of Equation 65. The sensitivity of the MM USSS isevaluated in the next section.

Noise Equivalent Radiometric Temperature of MM USSS

The Noise Equivalent Radiometric Temperature of the MM USSS {NERΔT}represent the minimum temperature the MM USSS can resolve, and it occursat a unity signals to noise ratio. Mathematically, this is obtained bydividing the noise voltage, given by Equation 65, by the absoluteresponsivity, given by Equation 33, and after some rearrangements andthe approximation that G₁<<G₂, we obtain:

$\begin{matrix}{{{NER}\;\Delta\; T} \geq {{\frac{G_{D1}}{G_{AE}}\begin{bmatrix}{{\left( \frac{G_{AE}}{G_{D1}} \right)^{2}\delta\; T_{SS}^{2}} + \left( \frac{{kT}_{HB}^{2}}{C_{1}} \right) + \left( \frac{{kT}_{D}^{2}}{C_{1}} \right) + \left( \frac{{kT}_{IN}^{2}}{C_{2}} \right) +} \\{\left( {\frac{1}{4R_{10}C_{10}} - {\frac{B}{\pi}{{Ln}\left\lbrack {\omega_{1}R_{10}C_{10}} \right\rbrack}}} \right)\left( {I_{N0}R_{10}\frac{g_{m}}{G_{m}}\frac{I_{H}}{G_{2}}} \right)^{2}}\end{bmatrix}}^{1/2}\left\lbrack \frac{1 + \left( \frac{\omega\; C_{1}}{G_{D1}} \right)^{2}}{1 + \left( \frac{\omega\; C_{2}}{G_{2}} \right)^{2}} \right\rbrack}^{1/2}} & (66)\end{matrix}$

The expression for the MM USSS sensitivity is given as a product ofthree terms: degradation due to thermal loading [G₁/G_(AE)], noise fromthermal fluctuations and electronic circuits, and a ‘ac’ factor whichrepresents the frequency response of the detector 10 and intermediatestage 16. We will proceed to address each one of these terms in detail.

The first term is the degradation in sensitivity produced by the thermalloading from G_(D1) versus the conductance between the detector andscene G_(AE). Since G₁/G_(AE)≈30, this represents a significantdegradation. Electrical-thermal feedback has reduced this fromG₁/G_(AE)≈2400 to G_(D1)/G_(AE)≈30. This represents almost a 100-foldimprovement over conventional approaches and clearly illustrates theexcellent reason for proposing the MM USSS, which is greatly improvedsensitivity.

The terms in the square bracket represent all the noise sources. We canneglect the first term because of the large attenuation factor in front[G_(AE)/G_(D1)]²≈1/900. The combination of the second, third, and fourthterm in the square bracket is readily evaluated since we know that frombefore that (KT_(D) ²/C₁)≅8×10⁻⁸ K². The heat bath 14 and intermediatestage temperatures 16 are approximated to be about the same as thedetector 10 [T_(D)≈T_(HB)≈T_(IN)] and 10 C₁≅C₂. Combining the second,third, and fourth term in the square brackets, we obtain an estimate ofabout 2×10⁻⁷ K². It should be noted that these three terms by themselveslimit the sensitivity to more that 0.013 K.

Unfortunately, this excellent performance is degraded by the electroniccircuit noise, given by the fifth term in the square brackets ofEquation 66. The degradation is readily estimated by substitutingnumerical values. By design, R₁₀≈10⁸, C₁₀≈1PF, G_(M)/G_(M)≈0.1,I_(H)/G₂≈10, B≈1 KHz and the white noise power spectral density of thebipolar amplifier 18 is [I_(N0)]²(8/3)EI_(H) and estimated as equal to4.3×10⁻²⁵. Combining all these, the electronic circuit noise termbecomes:

$\begin{matrix}{{{Electronic}\mspace{14mu}{Noise}} = {4.2 \times 10^{- 9}\left( {{2.5 \times 10^{3}} - {\frac{10^{3}}{\pi}{{Ln}\left\lbrack {10^{- 4}\omega_{1}} \right\rbrack}}} \right)K^{2}}} & (67)\end{matrix}$

The electronic noise includes white noise (first term) and 1/f noise(second term). The total noise depends on the low frequency operatingcorner ω₁ of the sensor. The 1/f noise term is the larger of the twonoise terms and depends on the operating corner ω₁. If we assume thatcalibration is performed once every hour, automatically, then the valueof Equation 67 becomes 3.2×10⁻⁵ K². This is much larger than the sum ofall the detector's thermal noise term of 2×10⁻⁷ K². Inserting thenumerical results from Equation 67 into Equation 66 we obtain anestimate for the radiometric temperature resolution and it is 0.2 K.This is represents a prediction of excellent performance for a MM USSS.

From the analyses presented above and the embodiment of the inventiondisclosed herein, it indicates that the present invention isparticularly adapted for passive MM wave imaging. Passive millimeterwave imaging offers several important features including seeing throughclothing, through clouds, and during rain. The former characteristicoffers application for home defense for remote weapons and explosivedetection. The latter characteristic offers improved visibility formilitary platforms deployed over land, in the air and at sea.

Furthermore, the sensor when made with a monolithic design, on a singlesilicon wafer, obviates the need of any microwave mixers. Such asimplification in circuitry will directly lead to a significantreduction in cost of fabricating millimeter wave imagers.

Having thus shown and described what is at present considered to be thepreferred embodiments of USSS pixel invention, it should be noted thatall modifications, changes and alterations coming within the spirit andscope of the invention as set forth in the appended claims are alsomeant to be included.

1. An electromagnetic radiation sensor assembly, comprising: a heatbath; an antenna element for receiving radiant electromagnetic energy; athermally responsive absorber element coupled to the antenna element andincluding means for absorbing and detecting radiant electromagneticenergy received by said antenna element; an intermediate stage forthermally isolating the absorber element from the heat bath, saidintermediate stage including at least two first and at least two secondthermal isolation members each having a predetermined thermalconductance interconnecting the absorber element to the intermediatestage and the intermediate stage to the heat bath, the first thermalisolation members being located between the absorber element and theintermediate stage and the second thermal isolation members beinglocated between the intermediate stage and the heat bath; anelectro-thermal feedback circuit incorporated into the intermediatestage for reducing the thermal conductivity between the absorber elementand the heat bath by causing the temperature of the intermediate stageto converge to the temperature of the absorber element when detectingelectromagnetic radiation, thus effectively causing the thermalconductance of the first thermal isolation members to attain a minimumconductance value and thereby improve the sensitivity of the radiationsensor towards the radiation limit; and wherein the electro-thermalfeedback circuit includes a heat generating amplifier including abipolar transistor integrated with the intermediate stage and means fordetecting the temperature difference between the absorber element andthe intermediate stage and generating an output voltage signal dependenton the received electromagnetic radiation to control the power generatedby the amplifier, wherein the heat generated by the transistor includedin the amplifier itself directly heats the intermediate stage inresponse to said temperature difference signal so as to equalize thetemperature between the absorber element and the intermediate stage. 2.A sensor assembly according to claim 1 wherein said sensor assemblycomprises a two-tier device and wherein said antenna element, saidabsorber element and said intermediate stage comprises substantiallyco-planar elements located above the heat bath.
 3. A sensor assemblyaccording to claim 2 wherein said intermediate stage includes a supportmember and, wherein said support member and said first and secondisolation members form a bridge for positioning the absorber elementabove the means providing a heat bath.
 4. A sensor assembly according toclaim 3 wherein said heat bath includes a substrate and an upper bodyportion on which the antenna element is mounted, said upper body portionincluding a cavity over which the intermediate stage and the absorberelement are located.
 5. A sensor assembly according to claim 2 whereinsaid amplifier including a bipolar transistor comprises an amplifier andwherein said means for detecting the temperature difference includesfirst and second diodes for respectively sensing the temperaturedifference between said absorber element and said intermediate stage. 6.A sensor assembly according to claim 5 wherein the first and seconddiodes are connected in back-to-back circuit relationship and to theamplifier inputs.
 7. A sensor assembly according to claim 1 wherein saidantenna element is located on an upper outer surface of said heat bath.8. A sensor assembly according to claim 7 wherein said intermediatestage includes a centralized opening therein and wherein said absorberelement is located in said opening.
 9. A sensor assembly according toclaim 1 wherein the assembly comprises an x-y sensor assembly includingx-y address readout circuits, and wherein said heat bath, said antennaelement, said absorber element and said intermediate stage form a singlepixel addressed by the x-y address readout circuits.
 10. A sensorassembly according to claim 9 wherein said predetermined region alsoincludes millimeter wave region of the electromagnetic spectrum.
 11. Asensor assembly according to claim 9 wherein said absorber elementcomprises a bolometer.
 12. A sensor assembly according to claim 9wherein said absorber element includes resistor means and temperaturesensor means, wherein said resistor means is ac coupled to the antennato receive and absorb the electromagnetic energy, and said temperaturesensor means is thermally coupled to the resistor means to monitor itstemperature.
 13. A sensor assembly according to claim 9 wherein saidpixel is fabricated in silicon.
 14. A sensor assembly according to claim9 wherein a plurality of said pixels are included in an array of pixels.15. A sensor assembly according to claim 1 wherein the spectral responseof at least one of the elements including said absorber element and saidantenna element is adjusted to operate in a predetermined region of theelectromagnetic spectrum, including at least the infrared region of theelectromagnetic spectrum.
 16. An electromagnetic radiation sensorassembly, comprising: an array of sensor pixels, each of said pixelsincluding, a heat sink in the form of a heat bath member, an antennaelement for receiving radiant electromagnetic energy mounted on the heatbath member, a thermally sensitive detector element coupled to theantenna element for detecting the radiant electromagnetic energy, anintermediate stage located between the detector element and the heatbath member, and a support structure for the intermediate stagecomprising at least two first thermal isolation members having apredetermined thermal and electrical conductance connecting the detectorelement to the intermediate stage and at least two second thermalisolation members having a predetermined thermal and electricalconductance connecting the intermediate stage to the common heat bathmember; an electro-thermal feedback circuit in the intermediate stagefor reducing the thermal conductivity between the detector element andthe heat bath member by causing the temperature of the intermediatestage to converge to the temperature of the detector element in responseto absorbed electromagnetic radiation, effectively causing the thermalconductance of the first thermal isolation members to attain a minimumconductance value and thereby improve thermal isolation and thus thesensitivity of the sensor element toward the radiation limit; and,wherein the electro-thermal feedback circuit includes a heat generatingamplifier, including a bipolar transistor, integrated with theintermediate stage as well as means for detecting the temperaturedifference between the detector element and the intermediate stage andgenerating a temperature difference signal for controlling the solidbipolar transistor and the heat generated thereby; and, wherein the heatgenerated by the bipolar transistor itself directly heats theintermediate stage in response to said temperature difference signal soas to converge the temperature of the intermediate stage to thetemperature of the detector element.
 17. An electromagnetic assemblyaccording to claim 16 wherein the antenna element, the detector element,the intermediate stage are substantially coplanar in a two tier assemblywith the heat bath.
 18. A sensor assembly according to claim 16 whereinsaid detector element comprises a bolometer.
 19. A sensor assemblyaccording to claim 16 wherein the spectral response of at least one ofthe elements including the detector element and the antenna element isadjusted to operate in a predetermined region of the electromagneticspectrum.
 20. A sensor assembly according to claim 19 wherein thepredetermined region includes the infrared and/or millimeter wave regionof the electromagnetic spectrum.
 21. An electromagnetic radiation sensorassembly, comprising: heat bath means; antenna means located on an outersurface of the heat bath means for receiving electromagnetic radiation;heat absorber means for detecting electromagnetic radiation received bythe antenna means; an intermediate stage located between the heat bathmeans and the heat absorber means; thermal isolation means locatedbetween the intermediate stage and the heat bath means and the heatabsorber means for thermally isolating the heat absorber means from theheat bath means; first means having a predetermined thermal andelectrical conductance for connecting the heat absorber means to thethermal isolation means, and second means having a predetermined thermaland electrical conductance for connecting the thermal isolation means tothe heat bath means; and, electro-thermal feedback circuit meansincorporated into the thermal isolation means for reducing the thermalconductivity between the heat absorber means and the heat bath means bycausing the temperature of the thermal isolation means to converge tothe temperature of the heat absorber means when detectingelectromagnetic radiation, effectively causing the thermal conductanceof the first means for connecting to attain a minimum conductance valueand thereby improve the sensitivity of the sensor assembly toward theradiation limit; wherein the electro-thermal feedback circuit meansincludes heat generating bipolar transistor amplifier means integratedwith the thermal isolation means, and means for detecting thetemperature difference between the heat absorber means and the thermalisolation means and generating a temperature difference signal forcontrolling the power delivered by the bipolar transistor amplifier tothe intermediate stage; and, wherein the heat generated by the bipolartransistor amplifier means directly heats the thermal isolation means inresponse to said temperature difference signal so as to equalize thetemperature between the heat absorber means and the intermediate stage.22. A sensor assembly according to claim 21 wherein said antenna means,said heat absorber means, and said thermal isolation means form atwo-tier sensor assembly.
 23. An electromagnetic radiation sensorassembly, comprising: heat bath means; antenna means located on the heatbath means for receiving electromagnetic radiation; heat absorber meansfor detecting electromagnetic radiation received by the antenna means;an intermediate stage located between the heat bath means and the heatabsorber means; thermal isolation means located between the intermediatestage and the heat bath means and the heat absorber means for thermallyisolating the heat absorber means from the heat bath means; first meanshaving a predetermined thermal and electrical conductance for connectingthe heat absorber means to the thermal isolation means, and second meanshaving a predetermined thermal and electrical conductance for connectingthe thermal isolation means to the heat bath means; and, electro-thermalfeedback circuit means incorporated into the thermal isolation means forreducing the thermal conductivity between the heat absorber means andthe heat bath means by causing the temperature of the thermal isolationmeans to converge to the temperature of the heat absorber means whendetecting electromagnetic radiation, effectively causing the thermalconductance of the first means for connecting to attain a minimumconductance value and thereby improve the sensitivity of the sensorassembly toward the radiation limit; wherein the electro-thermalfeedback circuit means includes heat generating amplifier meansintegrated with the thermal isolation means, and means for detecting thetemperature difference between the heat absorber means and the thermalisolation means and generating a temperature difference signal forcontrolling the power delivered by the amplifier means to theintermediate stage; and, wherein the heat generated by the amplifiermeans directly heats the thermal isolation means in response to saidtemperature difference signal so as to equalize the temperature betweenthe heat absorber means and the intermediate stage.
 24. A radiationsensor assembly according to claim 23 wherein the antenna means islocated on an outer surface of the heat bath means.
 25. A sensorassembly according to claim 23 wherein said antenna means, said heatabsorber means, and said thermal isolation means form a two-tier sensorassembly.
 26. An electromagnetic radiation sensor assembly, comprising:a heat bath; an antenna element mounted on the heat bath for receivingincident radiant electromagnetic energy; a thermally responsive absorberelement coupled to the antenna element and including means for absorbingand detecting radiant electromagnetic energy received by said antennaelement; an intermediate stage for thermally isolating the absorberelement from the heat bath, said intermediate stage including a supportmember and at least two first and at least two second thermal isolationmembers each having a predetermined thermal conductance interconnectingthe absorber element to the intermediate stage and the intermediatestage to the heat bath; wherein the support member and the first andsecond isolation members form a bridge for positioning the absorberelement above the heat bath; wherein the heat bath includes a substrateand an upper body portion on which the antenna element is mounted, theupper body portion including a cavity over which the intermediate stageand the absorber element are located; an electro-thermal feedbackcircuit incorporated into the intermediate stage for reducing thethermal conductivity between the absorber element and the heat bath bycausing the temperature of the intermediate stage to converge to thetemperature of the absorber element when detecting electromagneticradiation, thus effectively causing the thermal conductance of the firstthermal isolation members to attain a minimum conductance value andthereby improve the sensitivity of the radiation sensor towards theradiation limit; and wherein the electro-thermal feedback circuitincludes a heat generating amplifier and means for detecting thetemperature difference between the absorber element and the intermediatestage and generating an output voltage signal dependent on the receivedelectromagnetic radiation to control the power generated by theamplifier, wherein the heat generated by the amplifier itself directlyheats the intermediate stage in response to said temperature differencesignal so as to equalize the temperature between the absorber elementand the intermediate stage.
 27. A radiation sensor assembly according toclaim 26 wherein the heat generating amplifier includes semiconductoramplifier means.
 28. A radiation sensor assembly according to claim 27wherein said semiconductor amplifier means includes at least onesemiconductor amplifying device.
 29. A radiation sensor assemblyaccording to claim 28 wherein said at least one semiconductor amplifyingdevice comprises a transistor of a predetermined type integrated withthe intermediate stage.
 30. A radiation sensor assembly according toclaim 29 wherein the transistor comprises a bipolar transistor.